Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (5): 1219-1234.doi: 10.1007/s10473-019-0502-1

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ON THE DIMENSIONS OF SPACES OF HARMONIC FUNCTIONS WITH POLYNOMIAL GROWTH

Xiantao HUANG   

  1. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2018-07-27 Revised:2019-01-24 Online:2019-10-25 Published:2019-11-11
  • Supported by:
    The author is partially supported by NSFC (11701580 and 11521101) and the Fundamental Research Funds for the Central Universities (17lgpy13).

Abstract: In this paper, we obtain an estimate for the lower bound for the dimensions of harmonic functions with polynomial growth and a Liouville type theorem on manifolds with nonnegative Ricci curvature whose tangent cone at infinity is a unique metric cone with a conic measure.

Key words: Ricci curvature, harmonic function with polynomial growth, eigenvalue

CLC Number: 

  • 35A01
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