Results 41 to 50 of about 654,693 (352)
Uniqueness of two-convex closed ancient solutions to the mean curvature flow [PDF]
Annals of Mathematics, 2018 In this paper we consider closed non-collapsed ancient solutions to the mean curvature flow ($n \ge 2$) which are uniformly two-convex. We prove that any two such ancient solutions are the same up to translations and scaling.
S. Angenent +2 more
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Mean Curvature Flow of Mean Convex Hypersurfaces [PDF]
Communications on Pure and Applied Mathematics, 2016 In the last 15 years, White and Huisken‐Sinestrari developed a far‐reaching structure theory for the mean curvature flow of mean convex hypersurfaces. Their papers provide a package of estimates and structural results that yield a precise description of singularities and of high‐curvature regions in a mean convex flow.In the present paper, we give a ...
Robert Haslhofer, Bruce Kleiner
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A convergent evolving finite element algorithm for mean curvature flow of closed surfaces [PDF]
Numerische Mathematik, 2018 A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the discrete surface ...
Bal'azs Kov'acs, Buyang Li, C. Lubich
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Scherk-like translators for mean curvature flow [PDF]
Journal of differential geometry, 2019 We prove existence and uniqueness for a two-parameter family of translators for mean curvature flow. We get additional examples by taking limits at the boundary of the parameter space.
D. Hoffman, F. Mart'in, B. White
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Universality in mean curvature flow neckpinches [PDF]
Duke Mathematical Journal, 2015 We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is $C^3$-close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically rotationally symmetric in a space-time neighborhood of its singular set, and will have a unique ...
Gang, Zhou, Knopf, Dan
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Notes on Translating Solitons for Mean Curvature Flow [PDF]
Minimal Surfaces: Integrable Systems and Visualisation, 2019 The purpose of these notes is to provide an introduction to those who want to learn more about translating solitons for the mean curvature flow in $\mathbb{R}^3$, particularly those which are complete graphs over domains in $\mathbb{R}^2$.
D. Hoffman +3 more
semanticscholar +1 more source
Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space
Abstract and Applied Analysis, 2014 Let f(x) be a smooth strictly convex solution of det(∂2f/∂xi∂xj)=exp(1/2)∑i=1nxi(∂f/∂xi)-f defined on a domain Ω⊂Rn; then the graph M∇f of ∇f is a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean space Rn2n with the indefinite metric ...
Ruiwei Xu, Linfen Cao
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Some Characterizations of Generalized Null Scrolls
Mathematics, 2019 In this work, a family of ruled surfaces named generalized null scrolls in Minkowski 3-space are investigated via the defined structure functions. The relations between the base curve and the ruling flow of the generalized null scroll are revealed.
Jinhua Qian +2 more
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Diameter Estimate in Geometric Flows
Mathematics, 2023 We prove the upper and lower bounds of the diameter of a compact manifold (M,g(t)) with dimRM=n(n≥3) and a family of Riemannian metrics g(t) satisfying some geometric flows. Except for Ricci flow, these flows include List–Ricci flow, harmonic-Ricci flow,
Shouwen Fang, Tao Zheng
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Blow-up of the mean curvature at the first singular time of the mean curvature flow [PDF]
Calculus of Variations and PDEs, June 2016, 55:65, 2013 It is conjectured that the mean curvature blows up at the first singular time of the mean curvature flow in Euclidean space, at least in dimensions less or equal to 7. We show that the mean curvature blows up at the singularities of the mean curvature flow starting from an immersed closed hypersurface with small L^2-norm of the traceless second ...
arxiv +1 more source