An Alexandrov-type theorem in warped product manifolds with radial density

Jinchuan Bai; Chao Xia

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arXiv · 2608.08548

An Alexandrov-type theorem in warped product manifolds with radial density

Jinchuan Bai·Chao Xia

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Abstract

In this paper, we establish a Heintze--Karcher inequality for closed embedded hypersurfaces in a class of warped product manifolds endowed with radial density. As a consequence, we prove Alexandrov-type theorem for constant weighted mean curvature hypersurfaces in such spaces. In particular, we prove that a closed embedded $\lambda$-self-expander in the Euclidean space must be a round sphere centered at the origin.

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Jinchuan Bai, Chao Xia. 2026-08-09. An Alexandrov-type theorem in warped product manifolds with radial density. https://arxiv.org/abs/2608.08548

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