On L-p-affine surface areas

Elisabeth Werner

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

Let K be a convex body in ℝnwith centroid at 0 and B be the Euclidean unit ball in ℝncentered at 0. We show that limt→0|K|-|Kt|/|B| _|Bt| =Op(K)/Op(B) where |K| respectively |B| denotes the volume of K respectively B, Op(K) respectively Op(B) is the p-affine surface area of K respectively B and {Kt}t≥0. {Bt)t≥0 are general families of convex bodies constructed from K, B satisfying certain conditions. As a corollary we get results obtained in [23,25,26,31]. Indiana University Mathematics Journal

Original languageEnglish (US)
Pages (from-to)2305-2323
Number of pages19
JournalIndiana University Mathematics Journal
Volume56
Issue number5
DOIs
StatePublished - 2007
Externally publishedYes

Keywords

  • Affine surface area

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