Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (1): 159-171.doi: 10.1016/S0252-9602(11)60217-8

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DEFORMING METRICS WITH POSITIVE CURVATURE BY A FULLY NONLINEAR FLOW

 YUE Yun, SHENG Wei-Min   

  1. China Mobile Group Zhejiang Co., Ltd., Hangzhou 310006, China|Department of Mathematics, Zhejiang University, Hangzhou 310027, China
  • Received:2007-11-06 Revised:2008-12-03 Online:2011-01-20 Published:2011-01-20
  • Supported by:

    Part of this article is the first author's bachelor thesis dissertation in Zhejiang University. Research supported by NSFC (10771189 and 10831008)

Abstract:

By studying a fully nonlinear flow deforming conformal metrics on a compact and connected manifold, we prove the long time existence and the exponential convergence of the solutions of the flow for any initial metric g0 with the Schouten tensor Ag0∈Γk.

Key words: Fully nonlinear flow, conformal metrics, Schouten tensor

CLC Number: 

  • 53C21
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