Calculus of Variations and Partial Differential Equations

, Volume 23, Issue 1, pp 33–50

Deforming metrics with negative curvature by a fully nonlinear flow


    • Institute of MathematicsChinese Academy of Sciences
  • Weimin Sheng
    • Institute of MathematicsChinese Academy of Sciences

DOI: 10.1007/s00526-004-0287-4

Cite this article as:
Li, J. & Sheng, W. Calc. Var. (2005) 23: 33. doi:10.1007/s00526-004-0287-4


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