JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (4): 83-86.doi: 10.6040/j.issn.1671-9352.0.2016.364

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Estimates for the Hessian of f-harmonic functions and their applications to splitting theorem

DENG Yi-hua   

  1. College of Mathematics and Statistics, Hengyang Normal University, Hengyang 421002, Hunan, China
  • Received:2016-07-23 Online:2017-04-20 Published:2017-04-11

Abstract: A new estimate for the Hessian of f-harmonic functions is obtained. Using the new estimate, we improve a splitting theorem on smooth metric measure space with weighted Poincaré inequality under the condition that the Bakry-Émery Ricci curvature is bounded from below by some negative functions.

Key words: smooth metric measure spaces, splitting theorem, weighted Poincaré inequality, f-harmonic function

CLC Number: 

  • O186.16
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