Uniqueness of free-boundary minimal hypersurfaces in rotational domains
Differential Geometry
2022-09-28 v2
Abstract
In this work, we investigate the existence of compact free-boundary minimal hypersurfaces immersed in several domains. Using an original integral identity for compact free-boundary minimal hypersurfaces that are immersed in a domain whose boundary is a regular level set, we study the case where this domain is a quadric or, more generally, a rotational domain. This existence study is done without topological restrictions. We also obtain a new gap theorem for free boundary hypersurfaces immersed in an Euclidean ball and in a rotational ellipsoid.
Keywords
Cite
@article{arxiv.2108.00441,
title = {Uniqueness of free-boundary minimal hypersurfaces in rotational domains},
author = {Ezequiel Barbosa and Allan Freitas and Rodrigo Melo and Feliciano Vitório},
journal= {arXiv preprint arXiv:2108.00441},
year = {2022}
}