Calculus of Variations and Partial Differential Equations

, Volume 23, Issue 1, pp 33-50

First online:

Deforming metrics with negative curvature by a fully nonlinear flow

  • Jiayu LiAffiliated withInstitute of Mathematics, Chinese Academy of Sciences Email author 
  • , Weimin ShengAffiliated withInstitute of Mathematics, Chinese Academy of Sciences

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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.