A local isoperimetric inequality for balls with nonpositive curvature
Differential Geometry
2026-02-20 v2 Metric Geometry
Abstract
We show that small perturbations of the metric of a ball in Euclidean n-space to metrics with nonpositive curvature do not reduce the isoperimetric ratio. Furthermore, the isoperimetric ratio is preserved only if the perturbation corresponds to a homothety of the ball. These results establish a sharp local version of the Cartan-Hadamard conjecture.
Keywords
Cite
@article{arxiv.2505.11971,
title = {A local isoperimetric inequality for balls with nonpositive curvature},
author = {Mohammad Ghomi and John Ioannis Stavroulakis},
journal= {arXiv preprint arXiv:2505.11971},
year = {2026}
}
Comments
8 pages; Minor revisions. Accepted for publication in Int. Math. Res. Not. (IMRN)