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arXiv · 2505.11971

A local isoperimetric inequality for balls with nonpositive curvature

Mohammad Ghomi·John Ioannis Stavroulakis
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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.

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Mohammad Ghomi, John Ioannis Stavroulakis. 2025-05-17. A local isoperimetric inequality for balls with nonpositive curvature. https://arxiv.org/abs/2505.11971

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