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The mean curvature flow in Minkowski spaces [PDF]
Science China Mathematics, 2018 Studying the geometric flow plays a powerful role in mathematics and physics. In this paper, we introduce the mean curvature flow on Finsler manifolds and give a number of examples of the mean curvature flow. For Minkowski spaces, a special case of Finsler manifolds, we will prove the existence and uniqueness for solution of the mean curvature flow and
, Zeng Fanqi, He Qun
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1999
In this paper, we introduce the linear scale-space theory for functions on finite graphs. This theory permits us to derive a discrete version of the mean curvature flow. This discrete version yields a deformation procedure for polyhedrons. The adjacent matrix and the degree matrix of a polyhedral graph describe the system equation of this polyhedral ...
Atsushi Imiya, Ulrich Eckhardt
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In this paper, we introduce the linear scale-space theory for functions on finite graphs. This theory permits us to derive a discrete version of the mean curvature flow. This discrete version yields a deformation procedure for polyhedrons. The adjacent matrix and the degree matrix of a polyhedral graph describe the system equation of this polyhedral ...
Atsushi Imiya, Ulrich Eckhardt
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Nucleation and mean curvature flow
Communications in Partial Differential Equations, 1998which is written in terms of the characteristic function of the evolving set. The argument is based on implicit time-discretization, derivation of uniform estimates, and passage to thIn this paper ...
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Parabolic Frequency for the Mean Curvature Flow
International Mathematics Research Notices, 2023Abstract This paper defines a parabolic frequency for solutions of the heat equation along homothetically shrinking mean curvature flows (MCFs) and proves its monotonicity along such flows. As a corollary, frequency monotonicity provides a proof of backwards uniqueness.
Baldauf, Julius +2 more
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Mean Curvature Flow and Isoperimetric Inequalities
2010The classical isoperimetric inequality in Euclidean space. Three different approaches.- The curve shortening flow and isoperimetric inequalities on surfaces.- $H^k$-flows and isoperimetric inequalities.- Estimates on the Willmore functional and isoperimetric inequalities.- Singularities in the volume-preserving mean curvature flow.- Bounds on the ...
RitoreĢ, M, SINESTRARI, CARLO
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SO(2) Symmetry of the Translating Solitons of the Mean Curvature Flow in $$\mathbb {R}^4$$
Annals of PDE, 2022Jingze Zhu
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Uniqueness of two-convex closed ancient solutions to the mean curvature flow
Annals of Mathematics, 2020Sigurd Angenent +1 more
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A planarity estimate for pinched solutions of mean curvature flow
Duke Mathematical Journal, 2022Keaton Naff
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Inverse anisotropic mean curvature flow and a Minkowski type inequality
Advances in Mathematics, 2017Chao Xia
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