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- Title
Volume Growth of Shrinking Gradient Ricci-Harmonic Soliton.
- Authors
Wu, Guoqiang; Zhang, Shijin
- Abstract
In this paper, we study the shrinking gradient Ricci-harmonic soliton. Firstly using Chow-Lu-Yang's argument, we give a necessary and sufficient condition for complete noncompact shrinking gradient Ricci-harmonic solitons with $$S\ge \delta $$ to have polynomial volume growth with order $$n-2\delta $$ . Secondly, we derive a Logarithmic Sobolev inequality, as an application, we prove that any noncompact shrinking gradient Ricci-harmonic soliton must have linear volume growth, generalizing previous result of Munteanu and Wang (Commun Anal Geom 20(1):55-94, 2012).
- Publication
Results in Mathematics / Resultate der Mathematik, 2017, Vol 72, Issue 1/2, p205
- ISSN
1422-6383
- Publication type
Article
- DOI
10.1007/s00025-017-0703-7