Gap results and existence of CMC free boundary hypersurfaces in rotational domains

Fuente: arXiv
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Main Authors: Freitas, Allan, Santos, Márcio, Sindeaux, J.
Format: Preprint
Published: 2023
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author Freitas, Allan
Santos, Márcio
Sindeaux, J.
author_facet Freitas, Allan
Santos, Márcio
Sindeaux, J.
contents In this paper, we work with the existence and uniqueness of free boundary constant mean curvature hypersurfaces in rotational domains. These are domains whose boundary is generated by a rotation of a graph. Under some conditions on the function that generates the graph and a gap condition on the umbilicity tensor, we classify the CMC free boundary hypersurfaces as topological disks or annulus. Also, we construct some examples of free boundary minimal surfaces in the rotational ellipsoid that, in particular, satisfy our gap condition.
format Preprint
id arxiv_https___arxiv_org_abs_2309_10405
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Gap results and existence of CMC free boundary hypersurfaces in rotational domains
Freitas, Allan
Santos, Márcio
Sindeaux, J.
Differential Geometry
In this paper, we work with the existence and uniqueness of free boundary constant mean curvature hypersurfaces in rotational domains. These are domains whose boundary is generated by a rotation of a graph. Under some conditions on the function that generates the graph and a gap condition on the umbilicity tensor, we classify the CMC free boundary hypersurfaces as topological disks or annulus. Also, we construct some examples of free boundary minimal surfaces in the rotational ellipsoid that, in particular, satisfy our gap condition.
title Gap results and existence of CMC free boundary hypersurfaces in rotational domains
topic Differential Geometry
url https://arxiv.org/abs/2309.10405