Fattening in mean curvature flow: Ars Inveniendi Analytica (2025), Paper No. 4, 32 pp.
Year: 2025
Type: article
Abstract: Read article For each g≥3, we prove existence of a compact, connected, smoothly embedded, genus-g surface Mg 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 Mg fattens at the first singular time. As g→∞, the shrinker converges to a multiplicity 2 plane. DOI: https://doi.org/10.15781/cybg-mf32
Source: Ars Inveniendi Analytica
Authors: Ilmanen, Tom, White, Brian
Institutions: ETH Zurich, Stanford University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7215134889