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Uniqueness of convex ancient solutions to mean curvature flow in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\m [PDF]
Inventiones Mathematicae, 2018 A well-known question of Perelman concerns the classification of noncompact ancient solutions to the Ricci flow in dimension 3 which have positive sectional curvature and are κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym ...
S. Brendle, K. Choi
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APPROXIMATION OF THE ANISOTROPIC MEAN CURVATURE FLOW [PDF]
Mathematical Models and Methods in Applied Sciences, 2007 In this paper, we provide simple proofs of consistency for two well-known algorithms for mean curvature motion, Almgren–Taylor–Wang's1 variational approach, and Merriman–Bence–Osher's algorithm.29 Our techniques, based on the same notion of strict sub- and superflows, also work in the (smooth) anisotropic case.
CHAMBOLLE A, NOVAGA, MATTEO
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Mean Curvature Type Flow with Perpendicular Neumann Boundary Condition inside a Convex Cone
Abstract and Applied Analysis, 2014 We investigate the evolution of hypersurfaces with perpendicular Neumann boundary condition under mean curvature type flow, where the boundary manifold is a convex cone.
Fangcheng Guo, Guanghan Li, Chuanxi Wu
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Mathematical and Computational Applications, 2019 We study a variational problem for hypersurfaces in the Euclidean space with an anisotropic surface energy. An anisotropic surface energy is the integral of an energy density that depends on the surface normal over the considered hypersurface, which was ...
Miyuki Koiso
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Local entropy and generic multiplicity one singularities of mean curvature flow of surfaces [PDF]
Journal of differential geometry, 2018 In this paper we prove that the generic singularity of mean curvature flow of closed embedded surfaces in $\mathbb R^3$ modelled by closed self-shrinkers with multiplicity has multiplicity one.
Ao Sun
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The mean curvature flow for isoparametric submanifolds [PDF]
Duke Mathematical Journal, 2009 A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere.
Liu, Xiaobo, Terng, Chuu-Lian
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Open Mathematics, 2020 In this paper, we discuss the monotonicity of the first nonzero eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow (MCF).
Qi Xuesen, Liu Ximin
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Collapsing of the line bundle mean curvature flow on Kähler surfaces [PDF]
, 2019 We study the line bundle mean curvature flow on Kähler surfaces under the hypercritical phase and a certain semipositivity condition. We naturally encounter such a condition when considering the blowup of Kähler surfaces.
Ryosuke Takahashi
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Uniformly Compressing Mean Curvature Flow [PDF]
The Journal of Geometric Analysis, 2018 Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a related geometric flow which is free of these drawbacks.
Wenhui Shi, Dmitry Vorotnikov
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PLoS ONE, 2015 PurposeFlow diverters (FD) are increasingly being considered for treating large or giant wide-neck aneurysms. Clinical outcome is highly variable and depends on the type of aneurysm, the flow diverting device and treatment strategies.
Jinyu Xu +7 more
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