Isomorphic Steiner symmetrization

• 成果类型: Article
• 署名作者: Klartag, MB; Milman, VD
• 署名单位: Tel Aviv University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-003-0290-y
• 发表日期: 2003
• 页码: 463-485
• 关键词: euclidean ball; convex-bodies; INEQUALITY

摘要

This paper proves that there exist 3n Steiner symmetrizations that transform any convex set K subset of R-n into an isomorphic Euclidean ball; i.e. if vol(K)=vol(D-n) where D-n is the standard Euclidean unit ball, then K can be transformed into a body (K) over tilde such that c(1)D(n) subset of (K) over tilde c(2)D(n), where c(1), c(2) are numerical constants. Moreover, for any c>2, cn symmetrizations are also enough.