Abstract

Gromov proved the following ''Limit theorem'': Let g be a Riemannian metric on a smooth manifold M (without boundary). If a sequence of Riemannian metrics on M converges to g in the ense, and each scalar curvature is bounded from below by k. Then the scalar curvature of the limiting metric g is also bounded from below by k. In this talk, I'd like to talk about some total-scalar-curvature-version theorems of this ''Limit theorem''. I also consider the limit theorem for certain weighted total scalar curvature and as its corollary, I give a definition of scalar curvature lower bound in a weak sense. To prove these, we use the Ricci flow and harmonic map heat flow with Ricci flow background. If I have time, I also would like to talk about limit theorems for the UPPER bound of total scalar curvatures. Compared to the above results, we use a different type of geometric flow: Yamabe flow.

 

WebEx Link: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m028387233f37afca0294021b9c8e3c41

Meeting number (access code): 2514 967 1439

Meeting password: rUWXJzdP433

 

Organizers: Nicolau Sarquis Aiex (NTNU), Chung-Jun Tsai (NTU), Siao-Hao Guo (NTU)