数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (5): 1219-1234.doi: 10.1007/s10473-019-0502-1

• 论文 • 上一篇    下一篇

ON THE DIMENSIONS OF SPACES OF HARMONIC FUNCTIONS WITH POLYNOMIAL GROWTH

黄显涛   

  1. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • 收稿日期:2018-07-27 修回日期:2019-01-24 出版日期:2019-10-25 发布日期:2019-11-11
  • 作者简介:Xiantao HUANG,E-mail:hxiant@mail2.sysu.edu.cn
  • 基金资助:
    The author is partially supported by NSFC (11701580 and 11521101) and the Fundamental Research Funds for the Central Universities (17lgpy13).

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).

摘要: 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.

关键词: Ricci curvature, harmonic function with polynomial growth, eigenvalue

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

中图分类号: 

  • 35A01