Rigidity of complete self-shrinkers whose tangent planes omit a nonempty set
Differential Geometry
2023-09-21 v2 Analysis of PDEs
Metric Geometry
Abstract
In this paper we prove rigidity results for the sphere, the plane and the right circular cylinder as the only self-shrinkers satisfying a classic geometric assumption, namely the union of all tangent affine submanifolds of a complete self-shrinker omits a non-empty set of the Euclidean space. This assumption lead us to a new class of submanifolds, different from those with polynomial volume growth or the proper ones. We also prove an analogous result for self-expanders.
Cite
@article{arxiv.2012.07104,
title = {Rigidity of complete self-shrinkers whose tangent planes omit a nonempty set},
author = {Hilário Alencar and Manuel Cruz and Gregório Silva Neto},
journal= {arXiv preprint arXiv:2012.07104},
year = {2023}
}
Comments
17 pages, 1 figure. Final version