Isoperimetric and total curvature inequalities in Cartan-Hadamard manifolds with nullity

Mohammad Ghomi

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arXiv · 2605.24638

Isoperimetric and total curvature inequalities in Cartan-Hadamard manifolds with nullity

Mohammad Ghomi

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Abstract

Using the Chern-Gauss-Bonnet theorem, we establish a sharp inequality for the total Gauss-Kronecker curvature of convex hypersurfaces in Cartan-Hadamard manifolds $M^n$ with nullity index at least $n-3$. Consequently, the Euclidean isoperimetric inequality extends to $M^n$, which proves the Cartan-Hadamard conjecture for these spaces.

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BibTeX RIS

Mohammad Ghomi. 2026-05-23. Isoperimetric and total curvature inequalities in Cartan-Hadamard manifolds with nullity. https://arxiv.org/abs/2605.24638

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