PreprintCC BY 4.0arXiv
Alexandrov's theorem in the anti-Gaussian space: A Reilly-formula approach
Abstract
We give an alternative proof of Alexandrov's theorem about constant weighted mean curvature hypersurfaces in the anti-Gaussian space, due to the authors and Johne-Silini independently, via a Reilly-type formula approach. Moreover, we establish a sharp Heintze-Karcher-type inequality for hypersurfaces in manifolds with a generalized substatic condition, together with its rigidity in Euclidean space with density.
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BibTeX
@misc{bai2026alexandrovs,
title = {{Alexandrov's theorem in the anti-Gaussian space: A Reilly-formula approach}},
author = {Jinchuan Bai and Chao Xia},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06406},
eprint = {2611.06406},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06406},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Alexandrov's theorem in the anti-Gaussian space: A Reilly-formula approach
AU - Jinchuan Bai
AU - Chao Xia
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06406
UR - https://arxiv.org/abs/2611.06406
AB - We give an alternative proof of Alexandrov's theorem about constant weighted mean curvature hypersurfaces in the anti-Gaussian space, due to the authors and Johne-Silini independently, via a Reilly-type formula approach. Moreover, we establish a sharp Heintze-Karcher-type inequality for hypersurfaces in manifolds with a generalized substatic condition, together with its rigidity in Euclidean space with density.
ER -