Affine surface area and convex bodies of elliptic type (Q484564)
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scientific article; zbMATH DE number 6384181
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Affine surface area and convex bodies of elliptic type |
scientific article; zbMATH DE number 6384181 |
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Affine surface area and convex bodies of elliptic type (English)
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7 January 2015
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A sufficiently smooth closed convex hypersurface is of elliptic type provided that its affine principal curvatures are positive. The author proves that if a convex body lies in a convex body of elliptic type and having the same affine surface area, then the two bodies coincide. This tightens the previous results on the matter by \textit{K. Leichtweiß} [Result. Math. 13, No. 3-4, 255--282 (1988; Zbl 0645.53004)] and \textit{E. Lutwak} [Adv. Math. 85, No. 1, 39--68 (1991; Zbl 0727.53016)].
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affine surface area
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convex body of elliptic type
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curvature image
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geominimal surface area
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