An Optimal Volume Growth Estimate for Noncollapsed Steady Gradient Ricci Solitons  

作　　者：Richard H.Bamler Pak-Yeung Chan Zilu Ma Yongjia Zhang 

机构地区：[1]Department of Mathematics,University of California Berkeley,Berkeley,CA,94720,USA [2]Department of Mathematics,University of California San Diego,La Jolla,CA,92093,USA [3]Department of Mathematics,Rutgers University,Piscataway,NJ,08854,USA [4]School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai,200240,China

出　　处：《Peking Mathematical Journal》2023年第2期353-364,共12页北京数学杂志（英文）

基　　金：R.H.Bamler was supported by NSF Grant DMS-1906500;Y.Zhang was supported by the starting-up grant of Shanghai Jiao Tong University.

摘　　要：In this paper,we prove a volume growth estimate for steady gradient Ricci solitons with bounded Nash entropy.We show that such a steady gradient Ricci soliton has volume growth rate no smaller than r^n+1\2.This result not only improves the estimate in(Chan et al.,arXiv:2107.01419,2021,Theorem 1.3),but also is optimal since the Bryant soliton and Appleton’s solitons(Appleton,arXiv:1708.00161,2017)have exactly this growth rate.

关 键 词：Ricci flow Ricci soliton Singularity model 

分 类 号：O17[理学—数学]