Liouville-type theorems on the complete gradient shrinking Ricci solitons

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 $L^p(p\ge 1\mathrm{or}0<p\le 1)$ Liouville theorems on the complete gradient shrinking Ricci solitons.

Add Example 0.8, some remarks and a reference

Cited by in corpus (1)

• A gap theorem on complete shrinking gradient Ricci solitons