Deforming metrics with negative curvature by a fully nonlinear flow

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Abstract.

By studying a fully nonlinear flow deforming conformal metrics on compact and connected manifold, we prove that for \(\lambda < 1\), any metric g with its modified Schouten tensor \(A^\lambda_{g}\in \Gamma_k^-\) always can be deformed in a natural way to a conformal metric with constant \(\sigma_k\)-scalar curvature at exponential rate.

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© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Institute of MathematicsChinese Academy of SciencesBeijingChina
  2. 2.Department of MathematicsZhejiang UniversityHangzhouChina

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