Einstein and conformally flat critical metrics of the volume functional

Pengzi Miao, Luen-Fai Tam

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35 Citations (Scopus)


Let R be a constant. Let M(gamma)(R) be the space of smooth metrics g on a given compact manifold Omega(n) (n >= 3) with smooth boundary Sigma such that g has constant scalar curvature R and g Sigma is a fixed metric gamma on Sigma. Let V (g) be the volume of g is an element of M(gamma)(R) In this work, we classify all Einstein or conformally flat metrics which are critical points of V(.) in M(gamma)(R).
Original languageEnglish
Pages (from-to)2907 - 2937
Number of pages31
JournalTransactions of the American Mathematical Society
Issue number6
Publication statusPublished - 2011

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