Einstein and conformally flat critical metrics of the volume functional

Pengzi Miao, Luen Fai Tam

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

Let R be a constant. Let MγR be the space of smooth metrics g on a given compact manifold Ωn (n ≥ 3) with smooth boundary S such that g has constant scalar curvature R and g|ε is a fixed metric γ on S. Let V (g) be the volume of g ε MγR . In this work, we classify all Einstein or conformally flat metrics which are critical points of V (.) in MγR.

Original languageEnglish (US)
Pages (from-to)2907-2937
Number of pages31
JournalTransactions of the American Mathematical Society
Volume363
Issue number6
DOIs
StatePublished - Jun 1 2011

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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