Rigidity theorems on hemispheres in non-positive space forms
Lan-Hsuan Huang, Damin Wu
TL;DR
This paper investigates curvature conditions that uniquely identify hemispheres in non-positive space forms, proving the Min-Oo conjecture for hypersurfaces in Euclidean and hyperbolic spaces.
Contribution
It establishes the Min-Oo conjecture for hypersurfaces in Euclidean and hyperbolic spaces, advancing understanding of curvature characterizations of hemispheres.
Findings
Proved the Min-Oo conjecture in Euclidean space
Proved the Min-Oo conjecture in hyperbolic space
Characterized curvature conditions for 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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Point processes and geometric inequalities