A classification of SL(n) invariant valuations

• 成果类型: Article
• 署名作者: Ludwig, Monika; Reitzner, Matthias
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 1219-1267
• 关键词: affine surface-area; minkowski-firey theory; l-p; convex hypersurfaces; multiplicative structure; stepwise approximation; l-0-minkowski problem; valued valuations; mixed volumes; bodies

摘要

A classification of upper semicontinuous and SL(n) invariant valuations on the space of n-dimensional convex bodies is established. As a consequence, complete characterizations of centro-affine and L-p affine surface areas are obtained. The proofs make use of a new SL(n) shaping process for convex bodies.