New Heintze-Karcher type inequalities in sub-static warped product manifolds

2025/04/21 by Li, Haizhong, Wei, Yong, Xu, Botong
#53C21 #53C24 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.15109

Abstract

In this paper, we prove Heintze-Karcher type inequalities involving the shifted mean curvature for smooth bounded domains in certain sub-static warped product manifolds. In particular, we prove a Heintze-Karcher-type inequality for non mean-convex domains in the hyperbolic space. As applications, we obtain uniqueness results for hypersurfaces satisfying a class of curvature equations.

Related

• The equality case in the substatic Heintze-Karcher inequality
• A Heintze-Karcher type inequality in hyperbolic space
• Weighted isoperimetric inequalities in warped product manifolds
• On rigidity of hypersurfaces with constant shifted curvature functions in warped product manifolds
• An integral formula and its applications on sub-static manifolds