Functional Covering Numbers

Shiri Artstein-Avidan, Boaz A. Slomka

Research output: Contribution to journalArticlepeer-review

Abstract

We define covering and separation numbers for functions. We investigate their properties, and show that for some classes of functions there is exact equality between separation and covering numbers. We provide analogues for various geometric inequalities on covering numbers, such as volume bounds, bounds connected with Hadwiger’s conjecture, and inequalities about M-positions for geometric log-concave functions. In particular we get strong versions of M-positions for geometric log-concave functions.

Original languageEnglish
Pages (from-to)1039-1072
Number of pages34
JournalJournal of Geometric Analysis
Volume31
Issue number1
DOIs
StatePublished - Jan 2021

Keywords

  • Covering numbers
  • Duality
  • Functionalization of geometry
  • Log-concave functions
  • M-position
  • Volume bounds

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