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A local isoperimetric inequality for balls with nonpositive curvature (2505.11971v1)
Published 17 May 2025 in math.DG and math.MG
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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