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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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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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Mean Curvature Flow in ${\cal{S}}$ -manifolds
Mathematical Physics, Analysis and Geometry, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A New Approach to the Analysis of Parametric Finite Element Approximations to Mean Curvature Flow
Foundations of Computational Mathematics, 2023Genming Bai, Buyang Li
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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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2021
In this survey article, we discuss recent developments on the mean curvature flow of graphical submanifolds, generated by smooth maps between Riemannian manifolds. We will see interesting applications of this technique, in the understanding of the homotopy type of maps between manifolds.
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In this survey article, we discuss recent developments on the mean curvature flow of graphical submanifolds, generated by smooth maps between Riemannian manifolds. We will see interesting applications of this technique, in the understanding of the homotopy type of maps between manifolds.
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Lagrangian mean curvature flow
2021Snapshots of modern mathematics from Oberwolfach;2021 ...
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