Uniqueness of convex ancient solutions to mean curvature flow in ℝ³

2017/11/02 by Simon Brendle, Kyeongsu Choi, Brendle, S. +1 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1711.00823

openalex publication_date 2017/11/02 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

A well-known question of Perelman concerns the classification of noncompact ancient solutions to the Ricci flow in dimension 3 which have positive sectional curvature and are κ-noncollapsed. In this paper, we solve the analogous problem for mean curvature flow in ℝ³, and prove that the rotationally symmetric bowl soliton is the only noncompact ancient solution of mean curvature flow in ℝ³ which is strictly convex and noncollapsed.

Cited by

• Uniqueness of ancient compact non-collapsed solutions to the\n 3-dimensional Ricci flow
• Ancient mean curvature flows and their spacetime tracks

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