A Heintze–Karcher Type Inequality in Hyperbolic Space

Yingxiang Hu; Yong Wei; Tailong Zhou

doi:10.1007/s12220-024-01553-5

A Heintze–Karcher Type Inequality in Hyperbolic Space

Yingxiang Hu
, Yong Wei^*
, Tailong Zhou

^*Corresponding author for this work

School of Mathematical Sciences

TU Wien
University of Science and Technology of China
Sichuan University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we prove a new Heintze–Karcher type inequality for shifted mean convex hypersurfaces in hyperbolic space. As applications, we prove an Alexandrov-type theorem for closed embedded hypersurfaces with constant shifted kth mean curvature in hyperbolic space. Furthermore, two uniqueness results for certain curvature equations are also obtained.

Original language	English
Article number	113
Journal	Journal of Geometric Analysis
Volume	34
Issue number	4
DOIs	https://doi.org/10.1007/s12220-024-01553-5
State	Published - Apr 2024

Keywords

53C21
53C24
53C42
Heintze–Karcher inequality
Hyperbolic space
Shifted principal curvatures
Unit normal flow

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10.1007/s12220-024-01553-5

Cite this

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abstract = "In this paper, we prove a new Heintze–Karcher type inequality for shifted mean convex hypersurfaces in hyperbolic space. As applications, we prove an Alexandrov-type theorem for closed embedded hypersurfaces with constant shifted kth mean curvature in hyperbolic space. Furthermore, two uniqueness results for certain curvature equations are also obtained.",

keywords = "53C21, 53C24, 53C42, Heintze–Karcher inequality, Hyperbolic space, Shifted principal curvatures, Unit normal flow",

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PY - 2024/4

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N2 - In this paper, we prove a new Heintze–Karcher type inequality for shifted mean convex hypersurfaces in hyperbolic space. As applications, we prove an Alexandrov-type theorem for closed embedded hypersurfaces with constant shifted kth mean curvature in hyperbolic space. Furthermore, two uniqueness results for certain curvature equations are also obtained.

AB - In this paper, we prove a new Heintze–Karcher type inequality for shifted mean convex hypersurfaces in hyperbolic space. As applications, we prove an Alexandrov-type theorem for closed embedded hypersurfaces with constant shifted kth mean curvature in hyperbolic space. Furthermore, two uniqueness results for certain curvature equations are also obtained.

KW - 53C21

KW - 53C24

KW - 53C42

KW - Heintze–Karcher inequality

KW - Hyperbolic space

KW - Shifted principal curvatures

KW - Unit normal flow

UR - https://www.scopus.com/pages/publications/85185962256

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A Heintze–Karcher Type Inequality in Hyperbolic Space

Abstract

Keywords

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