Surface bodies and \(p\)-affine surface area
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Publication:1877872
DOI10.1016/j.aim.2003.07.018zbMath1089.52002OpenAlexW2099636159MaRDI QIDQ1877872
Elisabeth M. Werner, Carsten Schuett
Publication date: 19 August 2004
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.aim.2003.07.018
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Cites Work
- Extended affine surface area
- Zur Affinoberfläche konvexer Körper. (On affine surfaces of convex bodies)
- Contributions to affine surface area
- On the \(p\)-affine surface area
- The distribution function of the convolution square of a convex symmetric body in \({\mathbb{R}{}}^ n\)
- On the regularity of solutions to a generalization of the Minkowski problem
- The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
- A characterization of affine surface area
- Affine perimeter and limit shape.
- The convex floating body.
- Random polytopes in smooth convex bodies
- The Santaló-regions of a convex body
- A general geometric construction for affine surface area
- Asymptotic estimates for best and stepwise approximation of convex bodies II
- Illumination bodies and affine surface area
- Random Polytopes and Affine Surface Area
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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