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A LOCAL UNIQUENESS THEOREM FOR MINIMIZERS OF PETTY’S CONJECTURED PROJECTION INEQUALITY
Published online by Cambridge University Press: 24 January 2018
Abstract
Employing the inverse function theorem on Banach spaces, we prove that in a $C^{2}(S^{n-1})$-neighborhood of the unit ball, the only solutions of $\unicode[STIX]{x1D6F1}^{2}K=cK$ are origin-centered ellipsoids. Here $K$ is an $n$-dimensional convex body, $\unicode[STIX]{x1D6F1}K$ is the projection body of $K$ and $\unicode[STIX]{x1D6F1}^{2}K=\unicode[STIX]{x1D6F1}(\unicode[STIX]{x1D6F1}K).$
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- Research Article
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- Copyright © University College London 2018
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