A note on Hang-Wang's hemisphere rigidity theorem

2019/05/06 by Lai, Mijia
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.01870

Abstract

Let (M,g) be a compact manifold with boundary and Ric_g≥ (n-1)g, Hang and Wang proved that (M,g) is isometric to the standard hemisphere if ∂ M is convex and isometric to \mathbbS^n-1(1). We prove some rigidity theorems when ∂ M is isometric to a product manifold where one factor is the standard sphere.

Related

• A Rigidity Theorem for the Hemisphere
• An elementary approach to some rigidity theorems
• Gelfand problem and Hemisphere rigidity
• Mean Curvature Rigidity and Non-rigidity Results on Spherical Caps
• Scalar curvature rigidity of the four-dimensional sphere