Frank Morgan | Academic Influence

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Frank Morgan

Mathematics

#1175

World Rank

#1971

Historical Rank

#500

USA Rank

Measure Theory

#960

World Rank

#1249

Historical Rank

#358

USA Rank

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Mathematics

Frank Morgan 's Degrees

PhD Mathematics Princeton University
Bachelors Mathematics Williams College

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Why Is Frank Morgan Influential?

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According to Wikipedia, Frank Morgan is an American mathematician and the Webster Atwell '21 Professor of Mathematics, Emeritus, at Williams College. He is known for contributions to geometric measure theory, minimal surfaces, and differential geometry, including the resolution of the double bubble conjecture. He was vice-president of the American Mathematical Society and the Mathematical Association of America.

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Frank Morgan 's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Geometric Measure Theory: A Beginner's Guide (1988) (812)
Streaming potential properties of westerly granite with applications (1989) (284)
Electromagnetic precursors to earthquakes in the Ulf band: A review of observations and mechanisms (1993) (242)
Manifolds with Density (2005) (240)
Proof of the Double Bubble Conjecture (2000) (205)
Electrokinetic dissipation induced by seismic waves (1991) (198)
Dielectric spectroscopy of sedimentary rocks (2001) (196)
Deriving the equations of motion for porous isotropic media (1992) (194)
On the isoperimetric problem in Euclidean space with density (2006) (179)
Regularity of isoperimetric hypersurfaces in Riemannian manifolds (2003) (144)
Some Sharp Isoperimetric Theorems for Riemannian Manifolds (2000) (136)
PAIRED CALIBRATIONS APPLIED TO SOAP FILMS, IMMISCIBLE FLUIDS, AND SURFACES OR NETWORKS MINIMIZING OTHER NORMS (1994) (127)
Riemannian geometry : a beginner's guide (1998) (123)
Modeling of streaming potential responses caused by oil well pumping (1994) (107)
Geometric measure theory (2009) (103)
Three-dimensional source inversion of self-potential data (2007) (96)
Three‐dimensional self‐potential inversion for subsurface DNAPL contaminant detection at the Savannah River Site, South Carolina (2007) (83)
Induced-polarization detection and mapping of contaminant plumes (2006) (81)
The Isoperimetric Problem on Surfaces (1999) (78)
Frequency-Dependent Streaming Potentials. (2001) (76)
Pore-scale modeling of electrical and fluid transport in Berea sandstone (2010) (76)
Dielectric constant determination using ground-penetrating radar reflection coefficients (2000) (73)
Geometric Measure Theory A Beginner ’ s Guide Fourth Edition (2008) (66)
Existence of isoperimetric regions in R n with density (2011) (61)
Hexagonal Economic Regions Solve the Location Problem (2002) (60)
Self potentials in cave detection (2002) (58)
Isoperimetric regions in cones (2002) (57)
Inversion for dielectric relaxation spectra (1994) (56)
Frequency-dependent electroosmosis. (2002) (55)
The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature (2000) (53)
Adaptive Moving Window Method for 3D P-Velocity Tomography and Its Application in China (2004) (52)
Clusters minimizing area plus length of singular curves (1994) (50)
Soap bubbles in ${\bf R}^2$ and in surfaces. (1994) (49)
Joint Seismic and Electrical Tomography (1997) (46)
SOAP BUBBLES IN R 2 AND IN SURFACES (1994) (45)
On the singular structure of two-dimensional area minimizing surfaces in ℝn (1982) (44)
Manifolds with Density and Perelman's Proof of the Poincaré Conjecture (2009) (43)
An isoperimetric comparison theorem for Schwarzschild space and other manifolds (2001) (41)
Myers' theorem with density (2006) (41)
OPEN PROBLEMS IN SOAP BUBBLE GEOMETRY (1996) (40)
Hydrogeophysical Methods for Analyzing Aquifer Storage and Recovery Systems (2010) (39)
Temperature-dependent streaming potentials: 1. Theory (2003) (39)
Minimal Surfaces, Crystals, Shortest Networks, and Undergraduate Research (1992) (36)
Isoperimetric comparison theorems for manifolds with density (2009) (36)
A method of fast, sequential experimental design for linearized geophysical inverse problems (2009) (35)
STABLE CONSTANT MEAN CURVATURE HYPERSURFACES ARE AREA MINIMIZING IN SMALL L 1 NEIGHBORHOODS (2008) (35)
Temperature-dependent streaming potentials: 2. Laboratory (2003) (35)
Area-minimizing surfaces, faces of Grassmannians, and calibrations (1988) (35)
Optimal city hierarchy: A dynamic programming approach to central place theory (2014) (35)
The layered shear-wave velocity structure of the crust and uppermost mantle in China (2008) (33)
The cone over the Clifford torus in R4 isΦ-minimizing (1991) (33)
Assessment of 2-D resistivity structures using 1-D inversion (1991) (31)
The Hexagonal Honeycomb Conjecture (1999) (30)
Size-minimizing rectifiable currents (1989) (30)
S wave tomography of the crust and uppermost mantle in China (2008) (30)
The standard double bubble is the unique stable double bubble in (2002) (29)
CHAPTER 1 – Geometric Measure Theory (1995) (29)
A regularity theorem for minimizing hypersurfaces modulo (1986) (29)
Existence of isoperimetric regions in $${\mathbb{R}^{n}}$$ with density (2013) (27)
In Situ, Nonlinear Soil Response Applying an Active Source (2009) (27)
Calibrations and New Singularities in Area-minimizing Surfaces: A Survey (1990) (26)
WHAT IS A SURFACE (1996) (25)
Electromagnetic cave-to-surface mapping system (2004) (25)
The exterior algebra ΛkRn and area minimization (1985) (25)
Comparison of four least-squares inversion schemes for studying equivalence in one-dimensional resistivity interpretation (1992) (25)
SOAP BUBBLES IN R2 AND IN SURFACES (2012) (25)
Permeability Estimation Using Spectral Induced Polarization Measurements (1999) (24)
Planar Wulff shape is unique equilibrium (2004) (24)
In polytopes, small balls about some vertex minimize perimeter (2004) (24)
Riemannian Geometry: A Beginners Guide, Second Edition (1998) (24)
Area-minimizing currents bounded by higher multiples of curves (1984) (23)
Mathematicians, Including Undergraduates, Look at Soap Bubbles (1994) (22)
Geodesic nets on the 2-sphere (1996) (22)
Lowersemicontinuity of energy clusters (1997) (22)
Examples of unoriented area-minimizing surfaces (1984) (21)
ON THE SINGULAR STRUCTURE OF THREE-DIMENSIONAL, AREA-MINIMIZING SURFACES' (1983) (21)
Singularities of Minimal Surfaces and Networks and Related Extremal Problems in Minkowski Space (1990) (20)
Isoperimetric curves on hyperbolic surfaces (1999) (20)
Almost every curve in R3 bounds a unique area minimizing surface (1978) (20)
Geodesics and soap bubbles in surfaces (1996) (18)
The faces of the Grassmannian of three-planes in R7 (Calibrated geometries on R7) (1986) (18)
Minimization of self-potential survey mis-ties acquired with multiple reference locations (2008) (17)
Curvy slicing proves that triple junctions locally minimize area (1996) (17)
On finiteness of the number of stable minimal hypersurfaces with a fixed boundary (1985) (16)
Wulff clusters inR2 (1998) (16)
Isoperimetric estimates in products (2006) (16)
( M , ɛ, δ)-Minimal Curve Regularity (1994) (16)
Investigations of andesitic volcanic debris terrains: Part 2 — Geotechnical (2006) (15)
Steiner and Schwarz symmetrization in warped products and fiber bundles with density (2009) (15)
Immiscible fluid clusters in R2 and R3. (1998) (14)
Isoperimetric Pentagonal Tilings (2011) (14)
1 – Geometric Measure Theory (2016) (14)
Self Potential Mapping Of Contaminants (1999) (14)
Induced polarization of shaly sands; salinity domain modeling by double embedding of the effective medium theory (1991) (14)
Direct method for determining constant corrections to geophysical survey lines for reducing mis-ties (1990) (14)
Instabilities of cylindrical bubble clusters (2002) (14)
Real analysis and applications : including Fourier series and the calculus of variations (2005) (14)
Measures on spaces of surfaces (1982) (13)
Non-uniqueness In Self-Potential Inversion (1996) (13)
Structure of the Upper Crust in Japan from S-Wave Attenuation Tomography (2009) (13)
THE INFLUENCE OF MICRO-GEOMETRY ON THE HYDRAULIC PERMEABILITY AND THE INDUCED POLARIZATION RESPONSE OF SANDSTONES (1998) (12)
3-D Induced Polarization Inversion using Complex Electrical Resistivit ies (1998) (12)
Fundamentals of streaming potentials in geophysics: Laboratory methods (1989) (12)
The Levy-Gromov Isoperimetric Inequality in Convex Manifolds with Boundary (2007) (12)
THE INFLUENCE OF PORE FLUID CHEMISTRY ON THE INDUCED POLARIZATION RESPONSE OF ROCKS AND SOILS (1998) (11)
Location Robustness of Earthquakes in Sichuan Province, China (2004) (11)
Instability of the wet x soap film (1998) (11)
minimal curve regularity (1994) (11)
Finite-Element Modeling of Streaming Potentials Due to Seepage: Study of a Dam (1991) (10)
Destabilization of the tetrahedral point junction by positive triple junction line energy (1991) (10)
Calibrations modulo v (1987) (10)
Surfaces minimizing area plus length of singular curves (1994) (10)
Reflection moveout inversion in azimuthally anisotropic media: accuracy, limitations and acquisition (1999) (9)
A smooth curve in R3 bounding a continuum of minimal manifolds (1981) (9)
A smooth curve in $\mathbf{R}^4$ bounding a continuum of area minimizing surfaces (1976) (8)
A note on cross‐profile morphology for glacial valleys (2005) (7)
Pressures inside bubbles in planar clusters (2007) (7)
Clusters with multiplicities in ℝ2 (2005) (7)
Mapping Of Tce And Pce Contaminant Plumes Using A 3-D Induced Polarization Borehole Data (2004) (7)
Induced Polariza Tion Imaging Of A Jet Fuel Plume (1999) (7)
Area-minimizing surfaces in cones (2002) (7)
A round ball uniquely minimizes gravitational potential energy (2005) (7)
Soap Bubble Clusters (1995) (6)
Are large perimeter- minimizing two-dimensional clusters of equal-area bubbles hexagonal or circular? (2013) (6)
Existence of least-perimeter partitions (2007) (6)
Colloquium : Soap bubble clusters (2007) (6)
Rotation in a Normed Plane (2007) (6)
Planar Clusters (2004) (5)
A sharp counterexample on the regularity of $\Phi $-minimizing hypersurfaces (1990) (5)
Resistivity In Cave Exploration (1999) (5)
The Gauss–Bonnet formula on surfaces with densities (2011) (5)
Isoperimetric balls in cones over tori (2009) (5)
Numerical Modeling of Transport Properties and Comparison to Laboratory Measurements (2008) (4)
Geodesics and soap bubbles in surfaces (1996) (4)
FERMAT'S LAST THEOREM, THE FOUR COLOR CONJECTURE, AND BILL CLINTON FOR APRIL FOOLS' DAY (1997) (4)
Least-volume representatives of homology classes in $G(2,\mathbf{C}^4)$ (1989) (4)
Soap Bubbles and Soap Films a (1990) (4)
Fermat's Last Theorem for Fractional and Irrational Exponents (2010) (4)
The Effects Of Antenna Orientation On Gpr Data Quality (2002) (4)
Cave Detection Using Gpr (1999) (4)
Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces inRn (2004) (4)
Gravity In Cave Exploration (1999) (4)
Isoperimetric Symmetry Breaking: a Counterexample to a Generalized Form of the Log-Convex Density Conjecture (2016) (4)
Measurements of the seismoelectric responses in a synthetic porous rock (2020) (3)
Are large two-dimensional clusters of perimeter-minimizing bubbles of equal-area hexagonal or circular? (2012) (3)
Induced Polarization In The Detection Of Cave Systems (1999) (3)
Hexagonal surfaces of Kapouleas (2004) (3)
An Approach For Simultaneously Inverting MT Data For Resistivity And Susceptibility (2005) (3)
Perimeter-minimizing curves and surfaces in $\mathbf{R}^n$ enclosing prescribed multi-volume (2000) (3)
When Soap Bubbles Collide (2004) (3)
On the Importance of Electrokinetic Forces In the Acoustics of Porous Media (1989) (3)
Some results on the phase behavior in coherent equilibria (1990) (3)
An isoperimetric inequality for the thread problem (1997) (3)
Double Bubble No More Trouble (2000) (3)
Isoperimetric Sets of Integers (2011) (3)
A REGULARITY THEOREM FOR MINIMIZING HYPERSURFACES MODULO v (2010) (3)
Minimal surfaces, crystals, and norms on Rn (1991) (3)
Cylindrical surfaces of delaunay (2004) (3)
Small Perimeter-Minimizing Double Bubbles in Compact Surfaces are Standard (2001) (3)
Frequency-Dependent Electro-osmosis (2002) (2)
Pressures in periodic foams (2004) (2)
Effects of Lateral Heterogeneity on 1D D.C. Resistivity and Transient Electromagnetic Soundings in Kuwait (2015) (2)
The Approximation Theorem (1988) (2)
Calibrations and the size of Grassmann faces (1992) (2)
3D Inversion of Induced Polarization Data From Borehole Measurements to Map Subsurface Contaminations of Tetrachloroethylene and Trichloroethylene. (2003) (2)
3D Self-Potential Inversion for Monitoring DNAPL Contaminant Distributions (2005) (2)
Antiferromagnetic Properties of NiO and CoO I. Symmetry Properties (1973) (2)
Spatial decision analysis of geothermal resource sites in the Qualibou Caldera, Saint Lucia, Lesser Antilles (2004) (2)
Re-evaluation of Pekeris' one-dimensional resistivity interpretation method (1990) (2)
The Isoperimetric Problem with Density (2017) (2)
To Bring Math to the World, Start with Mathematicians (2018) (2)
Geophysical and Geotechnical Investigations for Proposed Dominica Airport (2005) (2)
The symmetry group of a curve preserves a plane (1982) (2)
The Perfect Shape for a Rotating Rigid Body (2002) (2)
Velocity Measurement And Empirical Modeling In Sandstones (1986) (2)
Similarities in modeling groundwater flow and DC resistivity (1994) (2)
An instrument system for low-frequency (10−3–103 Hz) impedance measurements (1986) (2)
Seismic Measurements of Ground Displacements Caused by Trains and Quarry Blasts at the Superconducting Super Collider Site in Texas (2001) (2)
Resistivity Inversion Parameter Bounds In the Presence of Equivalence (1991) (2)
CLUSTERS WITH MULTIPLICITIES IN R 2 F (2005) (1)
Three Dimensional Self-Potential Inversion For Subsurface Contaminant Detection And Mapping At The Doe Savannah River Site, South Carolina (2004) (1)
3-D Spectral IP Imaging: Non-Invasive Characterization DE FG02 96ER 14714 (2000) (1)
Ground Penetrating Radar & Avo (1999) (1)
Reinterpretation of a vintage 4.5-km resistivity line through Sulphur Springs, St. Lucia (2002) (1)
Identification of Conductive Waste Bodies Using Borehole-to-Surface Electrical Resistivity Methods (1991) (1)
Effective Medium Approach to Critical Saturation (1991) (1)
Comments on ‘ Investigations of the variation of voltage gain with stability factor and biasing resistances in Darlington composite transistors ’ (1973) (1)
Detecting Underground Caves Using Joint Seismic And Electrical Imaging Method (1997) (1)
Antiferromagnetic properties of NiO and CoO. II. Paramagnon symmetries and magnon dispersion relations (1973) (1)
Is There Any Uniqueness And/or Resolution In Resistivity Inversion? (1989) (1)
Non-linear constraints with application to self-potential source inversion (2006) (1)
Volume Determination of Buried Sand Using Dc Resistivity: An Engineering Geophysics Case History (1990) (1)
Three-Dimensional Electrical Resistivity Tomography And Its Application To Larderello-Valle Secolo Geothermal Field In Tuscany, Italy (1997) (1)
Self Potential Monitoring Of Jet Fuel Air Sparging (1999) (1)
Novel approach for 1D resistivity inversion using the systematically determined optimum number of layers (2017) (1)
Investigations into groundwater flow towards a spring in the Saphire Area, Soufriere, St Lucia, West Indies (2019) (1)
INDUCED POLARIZATION WITH ELECTROMAGNETIC COUPLING: 3D SPECTRAL IMAGING THEORY: EMSP PROJECT NO. 73836 (2003) (1)
Microgeometric Quantification of Sedimentary Rocks By Computer Image Analysis: A Preliminary Review (1989) (1)
Application of electrical resistivity tomography to image Harrison Caves in Barbados, West Indies (1997) (1)
COMMENTS ON “THE APPLICATION OF VHF MEASUREMENTS TO EARTH QUAKEPREDICTION” BY R.P. SINGH AND D. RANKIN* (1987) (1)
3-D Pore And Grain Size Distributions From 2-D Images: Fact Or Fiction? (1990) (1)
CHAPTER 3 – Lipschitz Functions and Rectifiable Sets (1995) (1)
Lipschitz Functions and Rectifiable Sets (1988) (1)
CHAPTER 12 – Miscellaneous Useful Results (1995) (1)
CLUSTERS WITH MULTIPLICITIES IN (2005) (1)
Examples of Area-Minimizing Surfaces (1988) (1)
CHAPTER 2 – Measures (1988) (1)
The isoperimetric problem in higher codimension (2012) (1)
Monotonicity and Oriented Tangent Cones (1988) (1)
18 – Manifolds with Density and Perelman’s Proof of the Poincaré Conjecture (2016) (1)
The Space of Planar Soap Bubble Clusters (2016) (1)
Compound soap bubbles, shotest networks, and minimal surfaces (1992) (1)
15 – The Hexagonal Honeycomb and Kelvin Conjectures (2016) (0)
The Regularity of Area-Minimizing Hypersurfaces (1988) (0)
A list of open problems in differential geometry (2019) (0)
Recollections of Fred Almgren (1998) (0)
Miscellaneous Useful Results (1988) (0)
16 – Immiscible Fluids and Crystals (2016) (0)
The torus lemma on calibrations, extended (1989) (0)
My Undercover Mission to Find Cairo Tilings (2019) (0)
For the minimal surface equation, the set of solvable boundary values need not be convex (1996) (0)
CHAPTER 4 – Normal and Rectifiable Currents (1995) (0)
On Being a Student of Almgren's (1997) (0)
20 – The Log-Convex Density Theorem (2016) (0)
CHAPTER 10 – The Regularity of Area-Minimizing Hypersurfaces (1995) (0)
Isoperimetry with density (2016) (0)
Bubbles and Tilings: Art and Mathematics (2014) (0)
Stochastic Calculus and the Nobel Prize Winning Black-Scholes Equation (2009) (0)
Kelvin's 100-year-old Bubble Conjecture Burst (1999) (0)
The soap-bubble-geometry contest (1997) (0)
13 – Soap Bubble Clusters (2016) (0)
Rebalance Every (15000/V)^(1/3) Years (2010) (0)
Flat Chains Modulo v , Varifolds, and (M, ɛ, δ)-Minimal Sets (1988) (0)
Mathematics and Optimal Form. By Stefan Hildebrandt and Anthony Tromba (1988) (0)
CHAPTER 17 – Isoperimetric Theorems in General Codimension (2000) (0)
CHAPTER 9 – Monotonicity and Oriented Tangent Cones (1995) (0)
CHAPTER 15 – The Hexagonal Honeycomb and Kelvin Conjectures (2000) (0)
Index to Volume 84 (1990) (0)
Normal and Rectifiable Currents (1988) (0)
Frequency Dependent Electrokinetic Studies of Rocks and Soils. (1997) (0)
CHAPTER 7 – The Approximation Theorem (1995) (0)
Determination of Near-Surface Anisotropy From Surface Electromagnetic Data (2001) (0)
Shaly sand induced‐polarization modeling by double embedding (1989) (0)
Deep Resistivity Tomographic Imaging of The Qualibou Caldera, Saint Lucia (2003) (0)
3-D spectral IP imaging: Non-invasive characterization of contaminant plumes. Annual progress report, September 15, 1996--September 14, 1997 (1997) (0)
CHAPTER 11 – Flat Chains Modulo v, Varifolds, and (M, ε, δ)-Minimal Sets (2000) (0)
Stability factors of Darlington transistors (1984) (0)
The Isoperimetric Problem with Density (2017) (0)
Depth determination of the Moho interface beneath the Tibetan plateau and other areas of China (2012) (0)
3-D Spectral IP Imaging: Non-Invasive Characterization of Contaminant Plumes (1998) (0)
The Compactness Theorem and the Existence of Area-Minimizing Surfaces (1988) (0)
Monotonicity theorems for two-phase solids (1993) (0)
Occurrence of streaming potentials due to oil well pumping (1992) (0)
Estimation of direction of remanent magnetization: An inverse method using the phase specrum of a magnetic anomaly (1989) (0)
P- And S-wave Tomographic Images of An Oil Reservoir At MIT's Michigan Test Site (1997) (0)
Comparison of variable radius and constant radium pore models in the acoustics or porous media (1990) (0)
19 – Double Bubbles in Spheres, Gauss Space, and Tori (2016) (0)
Quantifying the effects of unknown resistivity structure on self-potential data analysis (2006) (0)
Modifications to a Bison model 2350A resistivity meter (1985) (0)
CHAPTER 13 – Soap Bubble Clusters (2000) (0)
Flat Chains Modulo v , Varifolds, and (M, ε, δ)-Minimal Sets (1995) (0)
17 – Isoperimetric Theorems in General Codimension (2016) (0)
Experimental Design Applied to Borehole DC Resistivity (2007) (0)
Noninvasive Contaminant Site Characterization Using Geophysical Induced Polarization (2003) (0)
The Parsimonious Universe.By Stefan Hildebrandt and Anthony Tromba (1997) (0)
Feasibility of streaming potential measurements during hydrofracturing (1995) (0)
Dielectric and conductivity modeling of three‐phase mixtures in the frequency domain (1990) (0)
Acoustic tomography and 3-D resistivity imaging of grout filled waste cells (1997) (0)
Symmetry properties and dispersion relations in antiferromagnetic NiO and CoO (2008) (0)
PERIMETER-MINIMIZING CURVES AND SURFACES IN R ENCLOSING PRESCRIBED MULTI-VOLUME* (2016) (0)
3-D spectral IP imaging: Non-invasive characterization of contaminant plumes. 1998 annual progress report (1998) (0)
Pore Size Determination Using Frequency-Dependent Electro-Osmosis (2001) (0)
New Model for the Elastic Modulus for Saturated Porous Carbonate Rocks (2019) (0)
Survey of Regularity Results (1988) (0)
Investigations in groundwater flow toward a spring in the Saphire area, Soufriere, Saint Lucia, West Indies (2019) (0)
Gravity Survey At Harrison Caves, Barbados, West Indies (1997) (0)
Comparison of a Few Damped Least-squares Inversion Algorithms (1990) (0)
Ground penetrating radar in version for fracture orientation (1999) (0)
GPR Imaging of Harrison Caves In Barbados, West Indies (1997) (0)
Inexpensive, portable, digital data logger (1986) (0)
CHAPTER 6 – Examples of Area-Minimizing Surfaces (1995) (0)
Experimental Studies of Electrical Fields on a Breaking Rock Sample (2001) (0)
CHAPTER 8 – Survey of Regularity Results (1995) (0)
Joint inversion for an improved reservoir modeling and an accurate history matching (2021) (0)
In orbifolds, small isoperimetric regions are small balls (2006) (0)
Book review: “Visual Differential Geometry and Forms” by Tristan Needham (2022) (0)
Direct method for determining constant corrections to field values along individual geophysical survey lines for reducing mis‐ties (1989) (0)
(M, £, f5)-MINIMAL CURVE REGULARITY (2010) (0)
14 – Proof of Double Bubble Conjecture (2016) (0)
Short Note Structure of the Upper Crust in Japan from S-Wave (2009) (0)
Laboratory Study Of Frequency Dependent Streaming Potentials (1998) (0)
CHAPTER 14 – Proof of Double Bubble Conjecture (2000) (0)
CHAPTER 16 – Immiscible Fluids and Crystals (2000) (0)
A list of open problems in differential geometry (2019) (0)

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