Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Ghomi, Mohammad
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7162409737