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

 Recent Issues Vol. 299: 1  2 Vol. 298: 1  2 Vol. 297: 1  2 Vol. 296: 1  2 Vol. 295: 1  2 Vol. 294: 1  2 Vol. 293: 1  2 Vol. 292: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Special Issues Submission Guidelines Submission Form Contacts Author Index To Appear ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Other MSP Journals
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