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Computing Curvature, Mean Curvature and Weighted Mean Curvature
2022 IEEE International Conference on Image Processing (ICIP), 2022Traditional computing methods for curvatures require the image to be second-order differentiable. Such requirement is not always satisfied, especially at sharp edges.
Yuanhao Gong
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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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Collapsing ancient solutions of mean curvature flow
Journal of differential geometry, 2021We construct a compact, convex ancient solution of mean curvature flow in $\mathbb{R}^{n+1}$ with $O(1) \times O(n)$ symmetry that lies in a slab of width $\pi$.
T. Bourni +2 more
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Complete translating solitons to the mean curvature flow in ℝ3 with nonnegative mean curvature
American Journal of Mathematics, 2020:We prove that any complete immersed two-sided mean convex translating soliton $\Sigma\subset{\Bbb R}^3$ for the mean curvature flow is convex. As a corollary it follows that an entire mean convex graphical translating soliton in ${\Bbb R}^3$ is the ...
J. Spruck, Ling Xiao
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The Quarterly Journal of Mathematics, 1986
The ith mean curvature \(K_ i\) of a compact immersed submanifold of dimension n in \(E^ k\) is the normalized ith elementary symmetric function of the principal curvatures. The authors consider homothety- invariant integrals of functions of the \(K_ i\). They discuss lower bounds for these.
Kühnel, Wolfgang, Pinkall, Ulrich
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The ith mean curvature \(K_ i\) of a compact immersed submanifold of dimension n in \(E^ k\) is the normalized ith elementary symmetric function of the principal curvatures. The authors consider homothety- invariant integrals of functions of the \(K_ i\). They discuss lower bounds for these.
Kühnel, Wolfgang, Pinkall, Ulrich
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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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The basic component of the mean curvature of Riemannian foliations
For a Riemannian foliation % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0 ...
Jesús A. Álvarez López
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Lectures on mean curvature flow and related equations
The aim in these lectures is to study singularity formation, nonuniqueness, and topological change in motion by mean curvature.
T. Ilmanen
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