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On Brakke’s mean curvature flow
Sugaku Expositions, 2022The article represents an excellent exposition of a fascinating, resurgent field of research, by one of the main researchers in the domain. It starts from the basic physical intuition and motivation, proceeds through essential background material, such as the mean curvature flow, as well as crucial definitions and tools from geometric measure theory ...
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Riemannian Mean Curvature Flow
2005In this paper we explicitly derive a level set formulation for mean curvature flow in a Riemannian metric space. This extends the traditional geodesic active contour framework which is based on conformal flows. Curve evolution for image segmentation can be posed as a Riemannian evolution process where the induced metric is related to the local ...
Raúl San José Estépar +2 more
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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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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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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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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 ...
Ritoré, 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
exaly
Uniqueness of two-convex closed ancient solutions to the mean curvature flow
Annals of Mathematics, 2020Panagiota Daskalopoulos, Nataša Sesum
exaly
Mean curvature flow with pinched curvature integral
Differential Geometry and its ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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