Mathematics > Differential Geometry
arXiv:2605.24638 (math)
[Submitted on 23 May 2026]
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.
Submission history
From: Mohammad Ghomi [view email]
[v1]
Sat, 23 May 2026 15:59:21 UTC (10 KB)
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