On the Aleksandrov-Fenchel inequality and the stability of the sphere |
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Authors: | Randolf Arnold |
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Institution: | (1) Fachbereich Mathematik, Universität Dortmund, Postfach 500 500, D-4600 Dortmund 50 |
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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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