Immersed self-shrinkers

DOI10.1090/tran/6907zbMath1457.53072arXiv1306.2383OpenAlexW2963422092MaRDI QIDQ5348737

Gregory Drugan, Stephen James Kleene

Publication date: 21 August 2017

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.2383

zbMATH Keywords

mean curvature flowGauss-Bonnet formulaself-shrinkerbehavior of geodesics near Angenent's torusshape of graphical geodesics

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Flows related to mean curvature (53E10)

Related Items (20)

Examples of compact \(\lambda\)-hypersurfaces in Euclidean spaces ⋮ Vanishing theorems, higher order mean curvatures and index estimates for self-shrinkers ⋮ Rigidity of complete self-shrinkers whose tangent planes omit a nonempty set ⋮ Smooth compactness of 𝑓-minimal hypersurfaces with bounded 𝑓-index ⋮ Rigidity and gap results for low index properly immersed self-shrinkers in \(\mathbb{R}^{m + 1}\) ⋮ An immersed \(S^n \lambda\)-hypersurface ⋮ Entropy bounds for self-shrinkers with symmetries ⋮ Examples of compact embedded convex \(\lambda \)-hypersurfaces ⋮ Shrinking doughnuts via variational methods ⋮ Reilly's type inequality for the Laplacian associated to a density related with shrinkers for MCF ⋮ A survey of closed self-shrinkers with symmetry ⋮ Error Analysis for a Finite Difference Scheme for Axisymmetric Mean Curvature Flow of Genus-0 Surfaces ⋮ Ancient and eternal solutions to mean curvature flow from minimal surfaces ⋮ Bounds on the index of rotationally symmetric self-shrinking tori ⋮ Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds ⋮ Hopf-type theorem for self-shrinkers ⋮ $\boldsymbol{O(m) \times O(n)}$ -invariant homothetic solitons for inverse mean curvature flow in $\boldsymbol {\mathbb{R}^{m+n}}$ ⋮ Numerically computing the index of mean curvature flow self-shrinkers ⋮ Complete \(\lambda\)-hypersurfaces in Euclidean spaces ⋮ Entropy bounds, compactness and finiteness theorems for embedded self-shrinkers with rotational symmetry

Cites Work

• Unnamed Item
• Embedded self-similar shrinkers of genus 0
• Generic mean curvature flow. I: Generic singularities
• Construction of complete embedded self-similar surfaces under mean curvature flow. III
• Asymptotic behavior for singularities of the mean curvature flow
• Mean curvature evolution of entire graphs
• Construction of complete embedded self-similar surfaces under mean curvature flow. II
• The normalized curve shortening flow and homothetic solutions
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern.
• Singular nonlinear Cauchy problems
• Differential forms and applications. Transl. from the Portuguese
• Regularity theory for mean curvature flow
• Elliptic partial differential equations of second order
• A Bernstein type theorem for self-similar shrinkers
• Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem
• Self-similar solutions to the curve shortening flow
• Self-shrinkers with a rotational symmetry
• Construction of complete embedded self-similar surfaces under mean curvature flow. Part I.
• A stable manifold theorem for the curve shortening equation
• Computation of Self-Similar Solutions for Mean Curvature Flow
• An immersed 𝑆² self-shrinker
• Ordinary Differential Equations

This page was built for publication: Immersed self-shrinkers