Caffarelli-Kohn-Nirenberg inequality on metric measure spaces with applications

Alexandru Kristály, Shin ichi Ohta

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We prove that if a metric measure space satisfies the volume doubling condition and the Caffarelli-Kohn-Nirenberg inequality with the same exponent n ≥ 3, then it has exactly the n-dimensional volume growth. As an application, if an n-dimensional Finsler manifold of non-negative n-Ricci curvature satisfies the Caffarelli-Kohn-Nirenberg inequality with the sharp constant, then its flag curvature is identically zero. In the particular case of Berwald spaces, such a space is necessarily isometric to a Minkowski space.

Original languageEnglish
Pages (from-to)711-726
Number of pages16
JournalMathematische Annalen
Volume357
Issue number2
DOIs
Publication statusPublished - Oct 1 2013

Keywords

  • 35R06
  • 53C60
  • 58J60

ASJC Scopus subject areas

  • Mathematics(all)

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