本刊英文版2023年66卷第6期(1141-1394)摘要  

出　　处：《中国科学：数学》2023年第6期I0002-I0005,共4页Scientia Sinica：Mathematica

摘　　要：Weak scalar curvature lower bounds along Ricci flow Wenshuai Jiang,Weimin Sheng&Huaiyu Zhang Abstract In this paper,we study Ricci fow on compact manifolds with a continuous initial metric.It was known from Simon(2002)that the Ricci flow exists for a short time.We prove that the scalar curvature lower bound is preserved along the Ricci fow if the initial metric has a scalar curvature lower bound in the distributional sense provided that the initial metric is Wl.p for some n<p≤co.As an application,we use this result to study the relation between the Yamabe invariant and Ricci fat metrics.We prove that if the Yamabe invariant is nonpositive and the scalar curvature is nonnegative in the distributional sense,then the manifold is isometric to a Ricci flat manifold.

关 键 词：CURVATURE INVARIANT RICCI 

分 类 号：O1-5[理学—数学] Z89[理学—基础数学]