Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (5): 1614-1618.doi: 10.1016/S0252-9602(10)60154-3

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GRADIENT ESTIMATES FOR POSITIVE SMOOTH f-HARMONIC FUNCTIONS

 CHEN Li, CHEN Wen-Yi   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2008-03-06 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    The research is supported by NSFC (10471108, 10631020).

Abstract:

For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below, generalizing the classical ones of Yau (i.e., when f is constant).

Key words: gradient estimate, f-harmonic function, Bakry-Emery Ricci tensor

CLC Number: 

  • 35K05
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