A total curvature estimate of closed hypersurfaces in non-positively curved symmetric spaces
Jiangtao Li, Zuo Lin, Liang Xu
TL;DR
This paper establishes a total curvature estimate for closed hypersurfaces in non-positively curved symmetric spaces, leading to an isoperimetric inequality, advancing geometric analysis in these curved spaces.
Contribution
It provides the first total curvature estimate for hypersurfaces in non-positively curved symmetric spaces and derives a related isoperimetric inequality.
Findings
Total curvature estimate for hypersurfaces
Isoperimetric inequality in non-positively curved spaces
Advancement in geometric analysis
Abstract
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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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Point processes and geometric inequalities