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On an extension of the Blaschke–Santaló inequality and the hyperplane conjecture

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
344
Issue
1
Identifiers
DOI: 10.1016/j.jmaa.2008.03.002
Keywords
  • Convex Bodies
  • Asymptotic Geometric Analysis
  • Blaschke–Santaló
  • Hyperplane Conjecture

Abstract

Abstract Let K be a symmetric convex body and K ○ its polar body. Call ϕ ( K ) = 1 | K | | K ○ | ∫ K ∫ K ○ 〈 x , y 〉 2 d y d x . It is conjectured that ϕ ( K ) is maximum when K is an ellipsoid. In particular this statement implies the Blaschke–Santaló inequality and the hyperplane conjecture. We verify this conjecture when K is restricted to be a p-ball.

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