Liouville-type theorems on the complete gradient shrinking Ricci solitons

Huabin Ge; Shijin Zhang

Liouville-type theorems on the complete gradient shrinking Ricci solitons

Differential Geometry 2016-10-11 v2

Authors: Huabin Ge , Shijin Zhang

Abstract

We prove that there does not exist non-constant positive $f$ -harmonic function on the complete gradient shrinking Ricci solitons. We also prove the $L^{p}(p\geq 1 \ {\rm or}\ 0<p\leq 1)$ Liouville theorems on the complete gradient shrinking Ricci solitons.

Keywords

liouville theorem ricci solitons

Cite

@article{arxiv.1609.09806,
  title  = {Liouville-type theorems on the complete gradient shrinking Ricci solitons},
  author = {Huabin Ge and Shijin Zhang},
  journal= {arXiv preprint arXiv:1609.09806},
  year   = {2016}
}

Comments

Add Example 0.8, some remarks and a reference

Related papers

View all related →