Stability of the Volume Preserving Mean Curvature Flow in Hyperbolic Space

Huang, Zheng; Lin, Longzhi; Zhang, Zhou

doi:10.1007/s42543-023-00067-3

Peking Math J

2023

DOI: 10.1007/s42543-023-00067-3

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Stability of the Volume Preserving Mean Curvature Flow in Hyperbolic Space

Zheng Huang

Longzhi Lin

Zhou Zhang

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2024

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Cited by 1 publication

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Volume preserving mean curvature flow of L2-almost umbilical hypersurfaces in hyperbolic space

Li,

Xu,

Zhao

2024

Int. J. Math.

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In this paper, we study the stability of the volume preserving mean curvature flow of closed hypersurfaces in the hyperbolic space. We prove that an [Formula: see text]-almost umbilical hypersurface will be deformed to a totally umbilical hypersurface along the flow. Our result removes the assumption on the mean curvature in the theorems of Huang-Lin-Zhang [Peking J. Math. (2023)] and Leng-Xu-Zhao [Int. J. Math. (2014)].

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Volume preserving mean curvature flow of L2-almost umbilical hypersurfaces in hyperbolic space

Li,

Xu,

Zhao

2024

Int. J. Math.

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Stability of the Volume Preserving Mean Curvature Flow in Hyperbolic Space

Cited by 1 publication

References 26 publications

Volume preserving mean curvature flow of L2-almost umbilical hypersurfaces in hyperbolic space

Volume preserving mean curvature flow of L2-almost umbilical hypersurfaces in hyperbolic space

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