Convex Hypersurfaces in Hadamard Manifolds
Alexander A.Borisenko
TL;DR
This paper proves a theorem demonstrating an extremal property of Lobachevsky space within the class of simply connected Riemannian manifolds with nonpositive curvature, highlighting its unique geometric features.
Contribution
It establishes a new extremal property of Lobachevsky space among nonpositively curved manifolds, advancing understanding of geometric inequalities in such spaces.
Findings
Lobachevsky space has a unique extremal geometric property.
The theorem characterizes Lobachevsky space among nonpositively curved manifolds.
Results contribute to the theory of convex hypersurfaces in Hadamard manifolds.
Abstract
We prove a theorem about an extremal property of Lobachevsky space among simply connected Riemannian manifolds of nonpositive curvature
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Taxonomy
TopicsMathematics and Applications · Geometric and Algebraic Topology · Holomorphic and Operator Theory