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arxiv: 2501.17146 · v1 · pith:RLVB6IP2 · submitted 2025-01-28 · math.DG

A total curvature estimate of closed hypersurfaces in non-positively curved symmetric spaces

Jiangtao Li , Zuo Lin , Liang Xu This is my paper

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classification math.DG
keywords closedcurvaturecurvedestimatehypersurfacesnon-positivelyspacessymmetric
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In this paper, we prove a total curvature estimate of closed hypersurfaces in simply-connected non-positively curved symmetric spaces, and as a corollary, we obtain an isoperimetric inequality for such manifolds.

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    Proves sharp total Gauss-Kronecker curvature inequality for convex hypersurfaces in Cartan-Hadamard manifolds with nullity index ≥ n-3 via Chern-Gauss-Bonnet, extending the isoperimetric inequality and proving the Car...