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Volume Growth of Shrinking Gradient Ricci-harmonic soliton
WU Guoqiang 1,ZHANG Shi-Jin 2 * #
1.Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018
2.School of Mathematics and systems science, Beihang University, Beijing, 100191
*Correspondence author
#Submitted by
Subject:
Funding: NSFC（No.11301017）, SRFDP（No.20131102120031）
Opened online: 3 May 2017
Accepted by: none
Citation: WU Guoqiang,ZHANG Shi-Jin.Volume Growth of Shrinking Gradient Ricci-harmonic soliton[OL]. [ 3 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4728702
 
 
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 $Sgeq delta$ to have polynomial volume growth with order $n-2delta$. 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 ofMunteanu-Wang.
Keywords:Geometry; Ricci-harmonic soliton; Logarithmic Sobolev Inequalities; Volume growth
 
 
 

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