Fattening in mean curvature flow

2024/06/26 by Tom Ilmanen, Illmanen, Tom, Brian White +1 · 7 citations
Engineering · #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.15781/cybg-mf32

openalex publication_date 2024/06/26 · openalex created_date 2024/06/29 · openalex updated_date 2026/07/28

Abstract

For each g≥ 3, we prove existence of a compact, connected, smoothly embedded, genus-g surface M_g with the following property: under mean curvature flow, there is exactly one singular point at the first singular time, and the tangent flow at the singularity is given by a shrinker with genus (g-1) and with two ends. Furthermore, we show that if g is sufficiently large, then M_g fattens at the first singular time. As g→∞, the shrinker converges to a multiplicity 2 plane.

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