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On the Aleksandrov-Fenchel inequality and the stability of the sphere

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Abstract

LetF be a closed convex hypersurface in Euclideand-space with almost constantq-th mean curvatureH q (q=1, ...,d−1). The deviation ofF from a suitable sphere is estimated explicitely in terms of geometric quantities ofF. The proof depends on a new stability result on the Aleksandrov-Fenchel inequality, which improves a theorem of Schneider.

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  1. Fachbereich Mathematik, Universität Dortmund, Postfach 500 500, D-4600, Dortmund 50

    Randolf Arnold

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  1. Randolf Arnold
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Arnold, R. On the Aleksandrov-Fenchel inequality and the stability of the sphere. Monatshefte für Mathematik 115, 1–11 (1993). https://doi.org/10.1007/BF01311206

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  • DOI: https://doi.org/10.1007/BF01311206

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