Tobias Colding

Q: What Schools Are Affiliated With Tobias Colding

Tobias Colding is affiliated with the following schools: University of Luxembourg, Massachusetts Institute of Technology, University of Copenhagen, University of Pennsylvania

Tobias Colding's AcademicInfluence.com Rankings

Tobias Colding

Mathematics

#941

World Rank

#1640

Historical Rank

Geometry

#39

World Rank

#70

Historical Rank

Measure Theory

#1146

World Rank

#1466

Historical Rank

mathematics Degrees

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Mathematics

Tobias Colding's Degrees

PhD Mathematics University of Copenhagen

Why Is Tobias Colding Influential?

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According to Wikipedia, Tobias Holck Colding is a Danish mathematician working on geometric analysis, and low-dimensional topology. He is the great grandchild of Ludwig August Colding. Biography He was born in Copenhagen, Denmark, to Torben Holck Colding and Benedicte Holck Colding. He received his Ph.D. in mathematics in 1992 at the University of Pennsylvania under Chris Croke. Since 2005 Colding has been a professor of mathematics at MIT. He was on the faculty at the Courant Institute of New York University in various positions from 1992 to 2008. He has also been a visiting professor at MIT and at Princeton University and a postdoctoral fellow at MSRI . Colding lives in Cambridge, MA, with his wife and three children.

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Tobias Colding'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

On the structure of spaces with Ricci curvature bounded below. II (2000) (837)
Generic mean curvature flow I; generic singularities (2009) (580)
Lower bounds on Ricci curvature and the almost rigidity of warped products (1996) (556)
A Course in Minimal Surfaces (2011) (323)
Ricci curvature and volume convergence (1997) (289)
Sharp Holder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications (2011) (189)
On the singularities of spaces with bounded Ricci curvature (2002) (177)
HARMONIC FUNCTIONS ON MANIFOLDS (1997) (168)
The Calabi-Yau conjectures for embedded surfaces (2004) (158)
The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected (2002) (147)
The min--max construction of minimal surfaces (2003) (145)
Uniqueness of blowups and Łojasiewicz inequalities (2013) (135)
Harmonic functions with polynomial growth (1997) (114)
Smooth compactness of self-shrinkers (2009) (112)
LIOUVILLE THEOREMS FOR HARMONIC SECTIONS AND APPLICATIONS (1998) (108)
Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman (2003) (108)
The space of embedded minimal surfaces of fixed genus in a 3-manifold II; Multi-valued graphs in disks (2002) (108)
The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks (2002) (105)
The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains (2002) (103)
Large manifolds with positive Ricci curvature (1996) (103)
Shape of manifolds with positive Ricci curvature (1996) (102)
Lower Bounds for Nodal Sets of Eigenfunctions (2010) (94)
The round sphere minimizes entropy among closed self-shrinkers (2012) (89)
The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus (2005) (86)
Estimates for parametric elliptic integrands (2002) (84)
Width and finite extinction time of Ricci flow (2007) (83)
Weyl type bounds for harmonic functions (1998) (82)
On uniqueness of tangent cones for Einstein manifolds (2012) (77)
New monotonicity formulas for Ricci curvature and applications. I (2011) (67)
Linear growth harmonic functions on complete manifolds with nonnegative Ricci curvature (1995) (66)
Rigidity of generic singularities of mean curvature flow (2013) (66)
The singular set of mean curvature flow with generic singularities (2014) (57)
Embedded minimal disks: Proper versus nonproper—global versus local (2002) (50)
Characterization of Tangent Cones of Noncollapsed Limits with Lower Ricci Bounds and Applications (2011) (47)
Minimal Submanifolds (2005) (46)
An excursion into geometric analysis (2003) (46)
Sharp estimates for mean curvature flow of graphs (2003) (41)
Almost rigidity of warped products and the structure of spaces with Ricci curvature bounded below (1995) (39)
Mean curvature flow (2015) (38)
Embedded minimal surfaces in R n (2001) (37)
Monotonicity and its analytic and geometric implications (2012) (35)
Ricci curvature and monotonicity for harmonic functions (2012) (34)
Multivalued minimal graphs and properness of disks (2002) (32)
Embedded minimal surfaces without area bounds in 3 - manifolds (1998) (30)
Complexity of parabolic systems (2019) (30)
Width and mean curvature flow (2007) (29)
Disks that are double spiral staircases (2002) (28)
Examples of embedded minimal tori without area bounds (1999) (28)
Differentiability of the Arrival Time (2015) (26)
Spaces with Ricci curvature bounds. (1998) (24)
Constraints on singularities under Ricci curvature bounds (1997) (24)
Minimal surfaces and mean curvature flow (2011) (24)
GENERALIZED LIOUVILLE PROPERTIES OF MANIFOLDS (1996) (22)
On Function Theory on Spaces with a Lower Ricci Curvature Bound (1996) (22)
Lojasiewicz inequalities and applications (2014) (21)
On the structure of embedded minimal annuli (2002) (21)
Optimal bounds for ancient caloric functions (2019) (21)
Embedded minimal disks (2002) (20)
Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications (2007) (19)
Singular limit laminations, Morse index, and positive scalar curvature (2002) (19)
Complete properly embedded minimal surfaces in $\mathbf{R}^3$ (2001) (19)
Regularity of the Level Set Flow (2016) (16)
Lower Ricci curvature, branching and the bilipschitz structure of uniform Reifenberg spaces (2011) (15)
Stability and Ricci curvature (1995) (14)
Metrics without Morse index bounds (2002) (14)
Level set method for motion by mean curvature (2016) (13)
Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds (2014) (11)
Arnold‐Thom Gradient Conjecture for the Arrival Time (2017) (11)
Sharp frequency bounds for eigenfunctions of the Ornstein–Uhlenbeck operator (2017) (11)
Regularity of elliptic and parabolic systems. (2019) (11)
Geodesic laminations with closed ends on surfaces and Morse index; Kupka-Smale metrics (2002) (11)
Dynamics of closed singularities (2018) (10)
On the classification of Heegaard splittings (2015) (9)
Volumes for Eigensections (2003) (9)
A Gap theorem for ends of complete manifolds (1995) (8)
Liouville properties (2019) (7)
Singularity structure in mean curvature flow of mean-convex sets (2003) (7)
Convergence of embedded minimal surfaces without area bounds in three-manifolds (1998) (6)
Parabolic Frequency on Manifolds (2020) (6)
Mean curvature flow as a tool to study topology of 4-manifolds (2012) (5)
Optimal growth bounds for eigenfunctions (2021) (4)
Wandering Singularities (2018) (4)
In Search of Stable Geometric Structures (2019) (4)
Analytical Properties for Degenerate Equations (2018) (4)
Entropy and codimension bounds for generic singularities (2019) (3)
Monotonicity - analytic and geometric implications (2012) (3)
Removable singularities for minimal limit laminations (2000) (3)
Characterization of Tangent Cones of Noncollapsed Limits with Lower Ricci Bounds and Applications (2013) (3)
Singularities of Ricci flow and diffeomorphisms (2021) (3)
Surveys in Differential Geometry IX , International Press An excursion into geometric analysis (2003) (2)
On uniqueness of tangent cones for Einstein manifolds (2013) (2)
Aspects of Ricci Curvature (1997) (2)
Embedded solutions of the Plateau problem (2011) (1)
Singularities and diffeomorphisms (2022) (1)
MIN-MAX FOR SWEEPOUTS BY CURVES (2007) (1)
Minimal submanifolds: Encyclopedia of Mathematical Physics (2005) (1)
The structure of embedded minimal surfaces (2011) (0)
What are the shapes of embedded minimal surfaces and why (2005) (0)
Level set flow for motion by mean curvature (2016) (0)
Rigidity of generic singularities of mean curvature flow (2015) (0)
Eigenvalue lower bounds and splitting for modified Ricci flow (2023) (0)
3-manifold V; Fixed genus (2015) (0)
MIN-MAX FOR SWEEPOUTS BY CURVES TOBIAS H. COLDING AND WILLIAM P. MINICOZZI II (2007) (0)
Singularities and Diffeomorphisms Dedicated to Blaine Lawson with admiration by Tobias Holck Colding *† (2022) (0)
EMBEDDED MINIMAL DISKS WITH PRESCRIBED CURVATURE BLOWUP (2005) (0)
Proper versus nonproper - global versus local; Embedded minimal disks (2002) (0)
Curvature estimates and consequences (2011) (0)
Committee ranking (2015) (0)
2 3 A ug 2 00 2 DISKS THAT ARE DOUBLE SPIRAL STAIRCASES (2003) (0)
Sharp frequency bounds for eigenfunctions of the Ornstein–Uhlenbeck operator (2018) (0)
The singular set of mean curvature flow with generic singularities (2015) (0)
Minimal surfaces in three-manifolds (2011) (0)
Alice Silverberg Through the Cryptographer ’ s Looking-Glass , and What Alice Found (2016) (0)
Level set flow (2016) (0)
The beginning of the theory (2011) (0)
Weak convergence, compactness and applications (2011) (0)
Geometric methods in Heegaard theory (2020) (0)
Min-max constructions (2011) (0)
Level Set Method For Motion byMean Curvature (2016) (0)
Complexity of parabolic systems (2020) (0)
Arrival, Time of (2017) (0)
Editorial (2020) (0)
Ricci curvature and monotonicity for harmonic functions (2013) (0)

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What Schools Are Affiliated With Tobias Colding?

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Tobias Colding's Published Works

Published Works

Other Resources About Tobias Colding

What Schools Are Affiliated With Tobias Colding?

Tobias Colding's AcademicInfluence.com Rankings