Geometry of Two-dimensional Self-shrinkers

2015/05/01 by Lu Wang, Wang, Lu · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #advanced mathematical theories #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1505.00133

24 pages, 0 figure

arxiv created 2015/05/01 · openalex publication_date 2015/05/01 · arxiv updated 2015/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a local graphical theorem for two-dimensional self-shrinkers away from the origin. As applications, we study the asymptotic behavior of noncompact self-shrinkers with finite genus. Also, we show uniform boundedness on the second fundamental form of two-dimensional noncompact self-shrinkers with bounded mean curvature and uniform locally finite genus.

Citations

• Geometry of shrinking Ricci solitons

Cited by

• The extension problem of the mean curvature flow (I)

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• Asymptotic structure of self-shrinkers
• Self-shrinkers whose asymptotic cones fatten
• An unknottedness result for noncompact self shrinkers
• The rigidity theorems of self shrinkers