Convex sets in Hadamard manifolds.

DOI10.1016/S0926-2245(02)00102-XzbMath1034.53056WikidataQ115338151 ScholiaQ115338151MaRDI QIDQ1397838

Alexander A. Borisenko

Publication date: 6 August 2003

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

zbMATH Keywords

exponential mapsectional curvaturehorocyclehorosphereLobachevsky spacegeodesic linesimply connected Riemannian manifoldouter parallel hypersurface

Mathematics Subject Classification ID

Global submanifolds (53C40) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

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Cites Work

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• Asymptotic behavior of convex sets in the hyperbolic plane
• Geometry of horospheres
• Total curvatures of convex hypersurfaces in hyperbolic space
• Asymptotic behaviour of \(\lambda\)-convex sets in the hyperbolic plane
• Two problems on \(h\)-convex sets in the hyperbolic space
• Comparison theorems on convex hypersurfaces in Hadamard manifolds
• Relation between area and volume for \(\lambda\)-convex sets in Hadamard manifolds

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