Liouville property for $f$-harmonic functions with polynomial growth

Jia-Yong Wu

Liouville property for $f$-harmonic functions with polynomial growth

Differential Geometry 2018-12-04 v3 Analysis of PDEs

Authors: Jia-Yong Wu

Abstract

We prove a Liouville property for any $f$ -harmonic function with polynomial growth on a complete noncompact smooth metric measure space $(M,g,e^{-f}dv)$ when the Bakry-\'Emery Ricci curvature is nonnegative and its diameter of geodesic sphere has sublinear growth.

Keywords

Liouville property f-harmonic functions polynomial growth smooth metric measure space Bakry-Émery Ricci curvature geodesic sphere diameter

Cite

@article{arxiv.1610.03923,
  title  = {Liouville property for $f$-harmonic functions with polynomial growth},
  author = {Jia-Yong Wu},
  journal= {arXiv preprint arXiv:1610.03923},
  year   = {2018}
}

Comments

final version, accepted by Kyushu J. Math

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