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On the generalized mean curvature
Calculus of Variations and Partial Differential Equations, 2010We study some properties of graphs whose mean curvature (in distributional sense) is a vector Radon measure. In particular, we prove that the distributional mean curvature of the graph of a Lipschitz continuous function u is a measure if and only if the distributional divergence of T u is a measure.
E. Barozzi +2 more
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, 2020
Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can
S. Esedoglu
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Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can
S. Esedoglu
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The motion of a surface by its mean curvature
, 2015Kenneth Brakke studies in general dimensions a dynamic system of surfaces of no inertial mass driven by the force of surface tension and opposed by a frictional force proportional to velocity.
K. Brakke
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Mean Curvature Is a Good Regularization for Image Processing
IEEE transactions on circuits and systems for video technology (Print), 2019Ill-posed problems are very common in many image processing and computer vision tasks. To solve such problems, a regularization must be imposed. In this paper, we argue why mean curvature is a good regularization for these tasks. From a geometry point of
Yuanhao Gong
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II—mean curvature and weighted mean curvature
Acta Metallurgica et Materialia, 1992Abstract Several different formulations are in use for mean curvature (appropriate for isotropic surface free energy) and weighted mean curvature (appropriate for anisotropic surface free energy). These formulations are collected and described in this paper.
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Graphical translators for mean curvature flow
Calculus of Variations and Partial Differential Equations, 2018In this paper we provide a full classification of complete translating graphs in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage ...
David Hoffman +3 more
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Min–max theory for constant mean curvature hypersurfaces
Inventiones Mathematicae, 2017In this paper, we develop a min–max theory for the construction of constant mean curvature (CMC) hypersurfaces of prescribed mean curvature in an arbitrary closed manifold.
Xin Zhou, Jonathan J. Zhu
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Prescribing the Mean Curvature
2021This chapter provides conditions either necessary or sufficient for a given quantity (either a scalar function or a vector field) to be the mean curvature of a given foliation with respect to some Riemannian metric. The particular case of this quantity being identically zero (tautness) has been described separately.
Vladimir Rovenski, Paweł Walczak
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Mean Curvature Flow Solitons in the Presence of Conformal Vector Fields
Journal of Geometric Analysis, 2017In this paper we introduce and study a notion of mean curvature flow soliton in Riemannian ambient spaces general enough to encompass target spaces of constant sectional curvature, Riemannian products or, in increasing generality, warped product spaces ...
L. Alías, J. D. de Lira, M. Rigoli
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