A sharp Blaschke–Santaló inequality for α-concave functions

Liran Rotem

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We define a new transform on α-concave functions, which we call the ♯-transform. Using this new transform, we prove a sharp Blaschke–Santaló inequality for α-concave functions, and characterize the equality case. This extends the known functional Blaschke–Santaló inequality of Artstein-Avidan, Klartag and Milman, and strengthens a result of Bobkov. Finally, we prove that the ♯-transform is a duality transform when restricted to its image. However, this transform is neither surjective nor injective on the entire class of α-concave functions.

Original languageEnglish (US)
Pages (from-to)217-228
Number of pages12
JournalGeometriae Dedicata
Volume172
Issue number1
DOIs
StatePublished - Oct 1 2014

Keywords

  • Blaschke–Santaló inequality
  • Convexity
  • Log-concavity
  • α-Concavity

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