A general geometric construction for affine surface area

Elisabeth Werner

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Let K be a convex body in ℝn and B be the Euclidean unit ball in ℝn. We show that limt→0 |K| - |Kt|/|B| - |Bt| = as(K)/as(B), where as(K) respectively as(B) is the 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 [M-W], [Schm], [S-W] and [W].

Original languageEnglish (US)
Pages (from-to)227-238
Number of pages12
JournalStudia Mathematica
Volume132
Issue number3
DOIs
StatePublished - 1999

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