#### Vol. 296, No. 2, 2018

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Liouville theorems, volume growth, and volume comparison for Ricci shrinkers

### Li Ma

Vol. 296 (2018), No. 2, 357–369
##### Abstract

We study volume growth, a Liouville theorem for $f$-harmonic functions, and a volume comparison property of unit balls in complete noncompact gradient Ricci shrinkers and gradient steady Ricci solitons. We also study integral properties of $f$-harmonic functions and harmonic functions on complete manifolds, such as the Ricci–Einstein solitons.

##### Keywords
Ricci shrinkers, $f$-harmonic functions, Liouville theorem, volume comparison
##### Mathematical Subject Classification 2010
Primary: 53C21, 53C44, 53C25