Support functions and mean width for α-concave functions

Liran Rotem

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In this paper we extend some notions, previously defined for log-concave functions, to the larger domain of the so-called α-concave functions. We begin with a detailed discussion of support functions-first for log-concave functions, and then for general α-concave functions. We continue by defining mean width, and proving some basic results such as an Urysohn type inequality. Finally, we demonstrate how such geometric results can imply Poincaré type inequalities.

Original languageEnglish (US)
Pages (from-to)168-186
Number of pages19
JournalAdvances in Mathematics
Volume243
DOIs
StatePublished - Aug 20 2013

Keywords

  • Mean width
  • Support function
  • Urysohn
  • α-concavity

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