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Congruence theorems for capillary hypersurfaces and a substatic Heintze--Karcher inequality
Abstract
We prove congruence theorems for capillary hypersurfaces of Euclidean space supported on a hyperplane or on a sphere, extending a result of Ros for closed hypersurfaces. We also establish a Heintze--Karcher type inequality for capillary hypersurfaces in substatic manifolds.
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BibTeX
@misc{guimaraes2026congruence,
title = {{Congruence theorems for capillary hypersurfaces and a substatic Heintze--Karcher inequality}},
author = {Felippe Guimarães},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23304},
eprint = {2609.23304},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23304},
}
RIS
TY - UNPB
TI - Congruence theorems for capillary hypersurfaces and a substatic Heintze--Karcher inequality
AU - Felippe Guimarães
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23304
UR - https://arxiv.org/abs/2609.23304
AB - We prove congruence theorems for capillary hypersurfaces of Euclidean space supported on a hyperplane or on a sphere, extending a result of Ros for closed hypersurfaces. We also establish a Heintze--Karcher type inequality for capillary hypersurfaces in substatic manifolds.
ER -