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
Milestones
Received: 3 January 2017
Revised: 5 December 2017
Accepted: 2 March 2018
Published: 16 July 2018
Authors
Li Ma
School of Mathematics and Physics
University of Science and Technology Beijing
Beijing
China
Department of Mathematics
Henan Normal University
Xinxiang
China