Gerhard Huisken | Academic Influence

Gerhard Huisken's AcademicInfluence.com Rankings

Gerhard Huisken

Mathematics

#416

World Rank

#841

Historical Rank

Measure Theory

#1515

World Rank

#1887

Historical Rank

mathematics Degrees

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Mathematics

Gerhard Huisken's Degrees

PhD Mathematics University of Tübingen

Why Is Gerhard Huisken Influential?

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According to Wikipedia, Gerhard Huisken is a German mathematician whose research concerns differential geometry and partial differential equations. He is known for foundational contributions to the theory of the mean curvature flow, including Huisken's monotonicity formula, which is named after him. With Tom Ilmanen, he proved a version of the Riemannian Penrose inequality, which is a special case of the more general Penrose conjecture in general relativity.

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Gerhard Huisken'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

Flow by mean curvature of convex surfaces into spheres (1984) (1266)
Asymptotic-behavior for singularities of the mean-curvature flow (1990) (928)
The inverse mean curvature flow and the Riemannian Penrose Inequality (2001) (819)
Mean curvature evolution of entire graphs (1989) (431)
Interior estimates for hypersurfaces moving by mean curvature (1991) (429)
Convexity estimates for mean curvature flow and singularities of mean convex surfaces (1999) (339)
Calculus of Variations and Geometric Evolution Problems (1999) (330)
The volume preserving mean curvature flow. (1987) (292)
Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature (1986) (250)
Mean curvature flow singularities for mean convex surfaces (1999) (240)
Local and global behaviour of hypersurfaces moving by mean curvature (1993) (230)
Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature (1996) (209)
Ricci deformation of the metric on a Riemannian manifold (1985) (201)
Non-parametric mean curvature evolution with boundary conditions (1989) (184)
Geometric evolution equations for hypersurfaces (1999) (181)
Mean curvature flow with surgeries of two–convex hypersurfaces (2009) (177)
A distance comparison principle for evolving curves (1998) (131)
Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes (1991) (128)
The Riemannian Penrose inequality (1997) (117)
Higher regularity of the inverse mean curvature flow (2008) (92)
Deforming hypersurfaces of the sphere by their mean curvature (1987) (70)
A Bernstein result for minimal graphs of controlled growth (1990) (62)
Immersed hypersurfaces with constant Weingarten curvature (1989) (53)
Convex ancient solutions of the mean curvature flow (2014) (53)
Ancient solutions to the Ricci flow with pinched curvature (2009) (37)
THE n-DIMENSIONAL ANALOGUE OF THE CATENARY: EXISTENCE AND NONEXISTENCE (1990) (37)
Multi linear formulation of differential geometry and matrix regularizations (2010) (37)
Interior curvature estimates for hypersurfaces of prescribed mean curvature (1989) (26)
Evolution of Hypersurfaces by Their Curvature in Riemannian Manifolds (1998) (21)
FLOW OF REAL HYPERSURFACES BY THE TRACE OF THE LEVI FORM (1999) (20)
CAPILLARY SURFACES OVER OBSTACLES (1985) (20)
Discrete curvature and the Gauss-Bonnet theorem (2010) (19)
Mean curvature flow with surgery of mean convex surfaces in three-manifolds (2018) (16)
Evolution Equations in Geometry (2001) (15)
Inverse mean curvature evolution of entire graphs (2017) (12)
Pseudo-Riemannian Geometry in Terms of Multi-Linear Brackets (2013) (11)
The n-dimensional analogue of the catenary: Prescribed area (1996) (11)
On the classical geometry of embedded surfaces in terms of Poisson brackets (2010) (9)
Energy inequalities for isolated systems and hypersurfaces moving by their curvature (2002) (8)
Workshop on theoretical and numerical aspects of geometric variational problems (1991) (7)
Mean curvature flow with surgery of mean convex surfaces in $\mathbb{R}^3$ (2013) (6)
On the geometry of Kähler-Poisson structures (2011) (6)
On the classical geometry of embedded manifolds in terms of Nambu brackets (2010) (6)
On the geometry of K\"ahler-Poisson structures (2011) (5)
On pendent drops in a capillary tube (1983) (4)
Capillary surfaces in negative gravitational fields (1984) (4)
Mean-curvature contraction of convex hypersurfaces (1986) (3)
Geometric concepts for the mass in General Relativity (1999) (3)
MULTI-LINEAR FORMULATION OF DIFFERENTIAL GEOMETRY (2012) (2)
C1,1-regularity of solutions to variational inequalities (1984) (1)
A fully nonlinear flow for two-convex hypersurfaces in Riemannian manifolds (2017) (1)
Mean curvature evolution of closed hypersurfaces (1997) (1)
On the evolution of hypersurfaces along their inverse spacetime mean curvature (2022) (1)
An evolution equation for the isoperimetric problem (1997) (1)
Finitely many surgeries for mean curvature flow and Ricci flow (2005) (0)
Pseudo-Riemannian Geometry in Terms of Multi-Linear Brackets (2014) (0)
Mini-Workshop: Aspects of Ricci-Flow (2005) (0)
Heat diffusion in geometry (2016) (0)
THE ^-DIMENSIONAL ANALOGUE OF THE CATENARY: EXISTENCE AND NON-EXISTENCE (2004) (0)
Geometric flows and 3-manifolds : Oberwolfach Lecture 2005 (2007) (0)
Singularities of the meancurvature ﬂow (1997) (0)
An evolution of metrics by the Ricci curvature (1997) (0)
On the geometry of K (2011) (0)
Geometric Flows and 3-Manifolds (2007) (0)
Singularity formation in geometric evolution equations (1991) (0)
Geometric Partial Differential Equations : Theory , Numerics and Applications (2012) (0)
On a modified mean curvature flow (1986) (0)
On a modiﬁed mean curvature ﬂow (1987) (0)

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