Gaven Martin | Academic Influence

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Gaven Martin

Mathematics

#4841

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#6846

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Measure Theory

#2877

World Rank

#3420

Historical Rank

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Mathematics

Gaven Martin's Degrees

PhD Mathematics University of Auckland
Bachelors Mathematics University of Auckland

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Why Is Gaven Martin Influential?

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According to Wikipedia, Gaven John Martin FRSNZ FASL FAMS is a New Zealand mathematician. He is a Distinguished Professor of Mathematics at Massey University, the head of the New Zealand Institute for Advanced Study, the former president of the New Zealand Mathematical Society , and former editor-in-chief of the New Zealand Journal of Mathematics. He is a former Vice-President of the Royal Society of New Zealand [Mathematical, Physical Sciences Engineering and Technology. His research concerns quasiconformal mappings, regularity theory for partial differential equations, and connections between the theory of discrete groups and low-dimensional topology.

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Gaven Martin'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

Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Pms-48) (2009) (714)
Geometric Function Theory and Non-linear Analysis (2002) (673)
Quasiregular mappings in even dimensions (1993) (236)
Discrete Quasiconformal Groups I (1987) (161)
The Dynamics of Semigroups of Rational Functions I (1996) (140)
Extremal Mappings of Finite Distortion (2005) (125)
Riesz transforms and related singular integrals. (1995) (112)
Mappings of BMO–bounded distortion (2000) (102)
Deformations of Annuli with Smallest Mean Distortion (2010) (90)
QUASICONFORMAL AND BI-LIPSCHITZ HOMEOMORPHISMS, UNIFORM DOMAINS AND THE QUASIHYPERBOLIC METRIC (1985) (83)
THE LIOUVILLE THEOREM (1998) (82)
Commutators, collars and the geometry of Möbius groups (1994) (81)
The Beltrami Equation (2007) (77)
On discrete Möbius groups in all dimensions: A generalization of Jørgensen's inequality (1989) (68)
The quasihyperbolic metric and associated estimates on the hyperbolic metric (1986) (68)
Julia sets of rational semigroups (1996) (60)
An Introduction to the Theory of Higher-dimensional Quasiconformal Mappings (2017) (59)
Mappings ofBMO-distortion and beltrami-type operators (2002) (56)
Minimal co-volume hyperbolic lattices, I: The spherical points of a Kleinian group (2009) (49)
Inequalities for Möbius transformations and discrete groups. (1991) (49)
Local dynamics of uniformly quasiregular mappings (2004) (47)
Minimal co-volume hyperbolic lattices, II: Simple torsion in a Kleinian group (2012) (45)
Arithmeticity, Discreteness and Volume (1995) (45)
The Distortion Theorem for quasiconformal mappings, Schottky’s Theorem and holomorphic motions (1997) (42)
QUASIREGULAR SEMIGROUPS (2008) (40)
Iteration theory and inequalities for Kleinian groups (1989) (40)
Mappings of Finite Distortion: Ln logα L‐Integrability (2003) (37)
Stability and extremality in j⊘rgensen's inequality (1989) (37)
THE TEICHMÜLLER PROBLEM FOR MEAN DISTORTION (2009) (35)
Deformations with smallest weighted Lp average distortion and Nitsche‐type phenomena (2012) (34)
Precisely invariant collars and the volume of hyperbolic 3-folds (1998) (32)
Discrete quasiconformal groups that are not the quasiconformal conjugates of Möbius groups (1986) (31)
On the minimal volume hyperbolic 3–orbifold (1994) (31)
Two‐Generator Arithmetic Kleinian Groups II (1998) (28)
Lipschitz conditions in conformally invariant metrics (1991) (28)
Cusps, triangle groups and hyperbolic 3-folds (1993) (27)
GROUP ACTIONS OF THE 2-SPHERE (1989) (27)
Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane (2006) (26)
Holomorphic Motions (2003) (26)
The Hilbert-Smith conjecture for quasiconformal actions (1999) (25)
On discrete isometry groups of negative curvature (1993) (23)
Rigidity in holomorphic and quasiregular dynamics (2003) (23)
Quasiconformal homogeneity of hyperbolic manifolds (2005) (23)
Some properties of semigroups of rational functions (1996) (22)
Kleinian groups with real parameters (2001) (21)
The generalized Lichnerowicz problem: uniformly quasiregular mappings and space forms (2006) (19)
Balls in Hyperbolic Manifolds (1989) (19)
Attractors in quasiregular semigroups (1997) (18)
Wave Propagation in Periodic Media (2010) (18)
Branch sets of uniformly quasiregular maps (1997) (17)
Stoïlow factorization for quasiregular mappings in all dimensions (2010) (16)
THE SPECTRUM OF ELLIPTIC AXIAL DISTANCES IN KLEINIAN GROUPS (1998) (16)
What's new for the Beltrami equation? (2001) (16)
The volume of hyperbolic 3-folds with P-torsion, P ⩾ 6 (1999) (15)
Maximal symmetry groups of hyperbolic 3-manifolds (2006) (15)
Convergence and Mobius Groups (1988) (15)
On the Margulis constant for Kleinian groups, I curvature (1995) (15)
Discrete convergence groups (1987) (14)
6-torsion and hyperbolic volume (1993) (14)
Calculation of the Kirchhoff coefficients for the Helmholtz resonator (2009) (14)
On the Discreteness of the Free Product of Finite Cyclic groups (1997) (14)
$L^p$-integrability & weak type $L^{2}$-estimates for the gradient of harmonic mappings of $\mathbb D$ (2008) (14)
Axial distances in discrete Möbius groups. (1992) (13)
On Minimisers of $$L^p$$Lp-mean Distortion (2014) (13)
Harmonic degree 1 maps are diffeomorphisms: Lewy's theorem for curved metrics (2013) (12)
Quasiregular self-mappings of manifolds and word hyperbolic groups (2007) (12)
2-Generator arithmetic Kleinian groups III (2002) (12)
Maximal Symmetry Groups of Hyperbolic three-manifolds (2006) (12)
The Theory of Quasiconformal Mappings in Higher Dimensions, I (2013) (12)
COFINITELY HOPFIAN GROUPS, OPEN MAPPINGS AND KNOT COMPLEMENTS (2010) (11)
Cylinder and horoball packing in hyperbolic space (2005) (9)
Teichmuller Mappings, Quasiconformal Homogeneity, and Non-amenable Covers of Riemann Surfaces (2011) (9)
Quasiconformal groups with small dilatation I (2000) (9)
Some Universal Constraints for Discrete Möbius Groups (1991) (9)
PACKING STRIPS IN THE HYPERBOLIC PLANE (2003) (9)
All Kleinian groups with two elliptic generators whose commutator is elliptic (2003) (8)
The non-compact arithmetic generalised triangle groups (2001) (8)
Quasiconformal and affine groups (1989) (8)
Landau-Zener effect for a quasi-2D periodic sandwich (2011) (8)
Squeezing the Sierpinski sponge (2002) (8)
Quasiregular Families Bounded in $$L^p$$ and Elliptic Estimates (2018) (8)
Hyperbolic axes and elliptic fixed points in a fuchsian group (1997) (7)
Infinite Group Actions on Spheres (1988) (7)
Triangle subgroups of Kleinian groups (1996) (7)
Factorizations of Lebesgue measure via convolutions (1988) (6)
On the Geometry of Kleinian Groups (1998) (6)
Geodesics in hyperbolic $3$-folds. (1997) (6)
Holomorphic Motions, Schottky’s Theorem and an Inequality for Discrete Groups (1995) (6)
Convergence groups with an invariant component pair (1992) (5)
The Geometry and Arithmetic of Kleinian Groups (2013) (5)
The iterated commutator in a fuchsian group (1993) (5)
Volumes of hyperbolic 3-manifolds. Notes on a paper of Gabai, Meyerhoff, and Milley (2003) (5)
Polynomial Trace Identities in SL(2,C), Quaternion Algebras, and Two-generator Kleinian Groups (2019) (5)
Nondiscrete parabolic characters of the free group F2 : supergroup density and Nielsen classes in the complement of the Riley slice (2020) (4)
Limit Functions for Convergence Groups and Uniformly Quasiregular Maps (2006) (4)
Analytic continuation for Beltrami systems, Siegel's Theorem for UQR maps, and the Hilbert-Smith Conjecture (2002) (4)
Extending rational maps (2004) (4)
Random Kleinian Groups, II Two Parabolic Generators (2018) (4)
The (6,p)-arithmetic Hyperbolic Lattices in Dimension 3. (2011) (4)
The $L^p$ Teichm\"uller theory: Existence and regularity of critical points (2020) (3)
Chebyshev polynomials and inequalities for Kleinian groups (2021) (3)
The tension equation with holomorphic coefficients, harmonic mappings and rigidity (2013) (3)
Holomorphic motions and quasicircles (2013) (3)
Quasihyperbolic metric universal covers (2020) (3)
Higher regularity and uniqueness for inner variational equations (2020) (3)
Random ideal hyperbolic quadrilaterals, the cross ratio distribution and punctured tori (2018) (3)
Recent Results in the Geometry of Kleinian Groups (2003) (3)
Non-variational extrema of exponential Teichmüller spaces (2019) (3)
Essential singularities of quasimeromorphic mappings. (1993) (3)
AMBIENT QUASICONFORMAL HOMOGENEITY OF PLANAR DOMAINS (2010) (3)
Random Kleinian Groups I: Random Fuchsian Groups (2017) (2)
New Approaches to Modeling Elastic Media (2013) (2)
Conformal Mappings from the Upper Half Plane to Fundamental Domains on the Hyperbolic Plane (2003) (2)
Quasiconformal groups of compact type (2005) (2)
Super regularity for Beltrami systems (2019) (2)
Monotone Maps of Rn are Quasiconformal (2008) (2)
Concrete one complex dimensional moduli spaces of hyperbolic manifolds and orbifolds (2022) (2)
Quasiregular Mappings, Curvature & Dynamics (2011) (2)
Quasicircles as equipotential lines, homotopy classes and geodesics (2014) (2)
The Teichmüller problem for L^p-means of distortion (2021) (2)
Approximating Metal-Insulator Transitions (2014) (2)
Approximations of the Riley slice (2021) (2)
Extremal mappings of finite distortion and the Radon–Riesz property (2021) (2)
The combinatorics of Farey words and their traces (2022) (2)
Joint Feature Selection with Dynamic Spectral Clustering (2020) (2)
A zero-range model for localized boundary stress on a tectonic plate with dissipative boundary conditions (2012) (2)
Siegel's Problem in Three Dimensions An Introduction to the AMS– NZMS Maclaurin Lecture “Siegel’s Problem on Small Volume Lattices” (2016) (1)
Stream lines, quasilines and holomorphic motions (2014) (1)
Memories of Vaughan Jones (2021) (1)
Random lattices, punctured tori and the Teichmüller distribution (2018) (1)
Landau-Zener Phenomenon on a Double of Weakly Interacting Quasi- 2d Lattices (2010) (1)
Fred Gehring’s Mathematics (2014) (1)
A functional equation arising in the theory of convergence groups (1994) (1)
On the uniqueness of extremal mappings of finite distortion (2022) (1)
Quasiconformal groups with small dilatation II (2006) (1)
The Dispersion Function of a Quasi Two-Dimensional Periodic Sandwich using a Dirichlet-to-Neumann Map (2012) (1)
Complex dynamical systems (1994) (1)
The ( p , q )-arithmetic hyperbolic lattices ; p , q ≥ 6 (2015) (1)
Joint Robust Multi-view Spectral Clustering (2020) (1)
New models for deformations: Linear Distortion and the failure of rank-one convexity (2020) (1)
Solvable model of a localized boundary stress on the tectonic plate with dissapative boundary conditions (2011) (1)
Distortion and topology (2014) (1)
The continuous part of the axial distance spectrum for Kleinian groups (2020) (1)
Random Möbius groups, I : Random subgroups of PSL(2,R) (2019) (1)
Energy-minimal Principles in Geometric Function Theory. (2021) (1)
The (p, q)-arithmetic hyperbolic lattices; p, q greater than or equal to 6 (2015) (0)
Chapter 5. The Measurable Riemann Mapping Theorem: The Existence Theory Of Quasiconformal Mappings (2008) (0)
On irrational rotations in convergence groups of the $2$-sphere (1994) (0)
Chapter 13. Higher Integrability (2008) (0)
Chapter 15. Schauder Estimates For Beltrami Operators (2008) (0)
Chapter 9. Nonlinear Riemann Mapping Theorems (2008) (0)
A resonance interaction of seismogravitational modes on tectonic plates (2018) (0)
Frederick William Gehring, Life and Mathematics (2016) (0)
Siegel ’ s Problem in Three Dimensions (2016) (0)
Joint Robust Multi-view Spectral Clustering (2020) (0)
Fred Gehring’s Mathematics (2014) (0)
Chapter 8. Solving General Nonlinear First-Order Elliptic Systems (2008) (0)
Sir Vaughan Frederick Randal Jones (2021) (0)
The Generic Failure of Lower-semicontinuity for the Linear Distortion Functional (2023) (0)
Joint Feature Selection with Dynamic Spectral Clustering (2020) (0)
Chapter 14. Lp-Theory Of Beltrami Operators (2008) (0)
Chapter 17. PDEs Not Of Divergence Type: Pucci’S Conjecture (2008) (0)
A pr 1 99 5 Arithmeticity , Discreteness and Volume (2008) (0)
Subharmonic functions, conformal metrics, and CAT(0) (2022) (0)
Provisional chapter New Approaches to Modeling Elastic Media (2017) (0)
Measurable conformal mappings in space (1994) (0)
Stream lines, quasilines and holomorphic motions (2015) (0)
Appendix: Elements Of Sobolev Theory And Function Spaces (2008) (0)
Mathematische Annalen Quasiconformal homogeneity of hyperbolic manifolds (2004) (0)
The Geometry Of Quasiconformal Mappings (lipschitz, Geodesic, Uniform, Quasihyperbolic). (1985) (0)
Chapter 16. Applications To Partial Differential Equations (2008) (0)
Distortion and topology (2017) (0)
Chapter 18. Quasiconformal Methods In Impedance Tomography: Calderón’s Problem (2008) (0)
Julia sets of rational semigroups (1996) (0)
Hyperbolic Geometry and Quasiconformal Mappings (2005) (0)
Chapter 3. The Foundations Of Quasiconformal Mappings (2008) (0)
Chapter 21. Aspects Of The Calculus Of Variations (2008) (0)
Measurable conformal mappings in space ( The regularity theory of quasiregular mappings ) (2013) (0)
Chapter 11. A Quasilinear Cauchy Problem (2008) (0)
Projections in Moduli Spaces of the Kleinian Groups (2021) (0)
Abelian nondiscrete convergence groups in the plane (1994) (0)
Chapter 7. The Concept Of Ellipticity (2008) (0)
Chapter 6. Parameterizing General Linear Elliptic Systems (2008) (0)
Subharmonic functions, conformal metrics, and CAT(0) (2020) (0)
Chapter 19. Integral Estimates For The Jacobian (2008) (0)
Chapter 12. Holomorphic Motions (2008) (0)
Chapter 2. A Background In Conformal Geometry (2008) (0)
Chapter 10. Conformal Deformations And Beltrami Systems (2008) (0)
Chapter 20. Solving The Beltrami Equation: Degenerate Elliptic Case (2008) (0)
Topological regularity for solutions to the generalised Hopf equation (2023) (0)
Chapter 4. Complex Potentials (2008) (0)

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