Rigidity theorems on hemispheres in non-positive space forms

Abstract

We study the curvature condition which uniquely characterizes the hemisphere. In particular, we prove the Min-Oo conjecture for hypersurfaces in Euclidean space and hyperbolic space.

20 pages. Typos corrected and added in proof. Appeared in Comm. Anal. Geom

References in corpus (3)

• Rigidity of area-minimizing two-spheres in three-manifolds
• Area-minimizing projective planes in three-manifolds
• A Rigidity Theorem for the Hemisphere