Regularity of inverse mean curvature flow in asymptotically hyperbolic manifolds with dimension 3

• 作者: Yuguang Shi Jintian Zhu
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（6）
• 所属期刊栏目: Progress of Projects Supported by NSFC
• 页码范围: 1109-1126
• 页数: 18页
• 语种: 英文

摘要

By using the nice behavior of the Hawking mass of the slices of a weak solution of inverse mean curvature flow in three-dimensional asymptotically hyperbolic manifolds,we are able to show that each slice of the flow is star-shaped after a long time,and then we get the regularity of the weak solution of inverse mean curvature flow in asymptotically hyperbolic manifolds.As an application,we prove that the limit of the Hawking mass of the slices of a weak solution of inverse mean curvature flow with any connected C2-smooth surface as initial data in asymptotically anti-de Sitter-Schwarzschild manifolds with positive mass is greater than or equal to the total mass,which is completely different from the situation in the asymptotically fiat case.