Minimal surfaces and mean curvature flow

2011/02/07 by Tobias Colding, Colding, Tobias H., William P. Minicozzi +1
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1102.1411

openalex publication_date 2011/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss recent results on minimal surfaces and mean curvature flow, focusing on the classification and structure of embedded minimal surfaces and the stable singularities of mean curvature flow. This article is dedicated to Rick Schoen.

Citations

• An isoperimetric inequality with applications to curve shortening
• Gaussian densities and stability for some Ricci solitons
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• On the proof of the positive mass conjecture in general relativity
• Local Rigidity Theorems for Minimal Hypersurfaces
• Curvature estimates for minimal hypersurfaces
• Minimal Varieties in Riemannian Manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Related

• Lectures on mean curvature flow of surfaces
• Evolution of curves and surfaces by mean curvature
• General curvature flow without singularities
• Mean curvature flow without singularities
• When can minimal hypersurfaces be connected by mean curvature flow?