Smooth compactness of self-shrinkers

2009/07/15 by Tobias Colding, Colding, Tobias H., William P. Minicozzi +1 · 3 citations
Engineering · Mathematics · #Advanced Materials and Mechanics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.0907.2594

openalex publication_date 2009/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a smooth compactness theorem for the space of embedded self-shrinkers in \RR³. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a compactness result for the space of all singularities and it plays an important role in studying generic mean curvature flow.

Cited by

• Free boundary and capillary minimal surfaces in spherical caps I: Low genus
• First eigenvalue and nodal domains of the drift Laplacian on symmetric self-shrinkers in ℝ³
• Stability of weighted minimal hypersurfaces under a lower 1-weighted Ricci curvature bound

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