A Heintze-Karcher-type inequality for capillary hypersurfaces in a hyperbolic half-space

Yingxiang Hu; Yong Wei; Chao Xia; Tailong Zhou

doi:10.1016/j.jfa.2025.110970

A Heintze-Karcher-type inequality for capillary hypersurfaces in a hyperbolic half-space

Yingxiang Hu
, Yong Wei^*
, Chao Xia
, Tailong Zhou

^*此作品的通讯作者

数学科学学院

TU Wien
University of Science and Technology of China
Xiamen University
Sichuan University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

In this paper, we establish a Heintze-Karcher-type inequality for compact embedded capillary hypersurfaces in a hyperbolic half-space. The proof is based on a geodesic normal map flow with respect to a Finsler metric of Randers-type induced by a special Zermelo's navigation data. As an application, we obtain an Alexandrov-type theorem for compact embedded capillary hypersurfaces of constant higher-order mean curvature in a hyperbolic half-space.

源语言	英语
文章编号	110970
期刊	Journal of Functional Analysis
卷	289
期	6
DOI	https://doi.org/10.1016/j.jfa.2025.110970
出版状态	已出版 - 15 9月 2025

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10.1016/j.jfa.2025.110970

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title = "A Heintze-Karcher-type inequality for capillary hypersurfaces in a hyperbolic half-space",

abstract = "In this paper, we establish a Heintze-Karcher-type inequality for compact embedded capillary hypersurfaces in a hyperbolic half-space. The proof is based on a geodesic normal map flow with respect to a Finsler metric of Randers-type induced by a special Zermelo's navigation data. As an application, we obtain an Alexandrov-type theorem for compact embedded capillary hypersurfaces of constant higher-order mean curvature in a hyperbolic half-space.",

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AU - Hu, Yingxiang

AU - Wei, Yong

AU - Xia, Chao

AU - Zhou, Tailong

PY - 2025/9/15

Y1 - 2025/9/15

N2 - In this paper, we establish a Heintze-Karcher-type inequality for compact embedded capillary hypersurfaces in a hyperbolic half-space. The proof is based on a geodesic normal map flow with respect to a Finsler metric of Randers-type induced by a special Zermelo's navigation data. As an application, we obtain an Alexandrov-type theorem for compact embedded capillary hypersurfaces of constant higher-order mean curvature in a hyperbolic half-space.

AB - In this paper, we establish a Heintze-Karcher-type inequality for compact embedded capillary hypersurfaces in a hyperbolic half-space. The proof is based on a geodesic normal map flow with respect to a Finsler metric of Randers-type induced by a special Zermelo's navigation data. As an application, we obtain an Alexandrov-type theorem for compact embedded capillary hypersurfaces of constant higher-order mean curvature in a hyperbolic half-space.

KW - Alexandrov-type theorem

KW - Capillary hypersurfaces

KW - Heintze-Karcher inequality

KW - Hyperbolic space

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U2 - 10.1016/j.jfa.2025.110970

DO - 10.1016/j.jfa.2025.110970

M3 - 文章

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SN - 0022-1236

VL - 289

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 6

M1 - 110970

ER -

A Heintze-Karcher-type inequality for capillary hypersurfaces in a hyperbolic half-space

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