Scalar curvature of a metric with unit volume

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The problem of finding Riemannian metrics on a closed manifold with prescribed scalar curvature function is now fairly well understood from the works of Kazdan and Warner in 1970's ([10] and references cited in it). In this paper we shall consider the same problem under a constraint on the volume. For this purpose it is useful to introduce an invariant p(M) of a smooth closed manifold M, which will be called the Yamabe number of M, defined as the supremum of #(M, C) of all conformal classes C of Riemannian metrics on M,

Journal

  • Mathematische Annalen

    Mathematische Annalen 279 (2), 253-265, 1987-12

    Springer Science and Business Media LLC

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