Xianzhe Dai (UCSB)

Title:  On the Metric Stability of K\"ahler-Einstein Metrics

Abstract: In our previous work, we proved metric stability of a large class of 
Ricci flat metrics, namely, those with special holonomy. A crucial 
ingredient is the use of parallel spinor, which dictates that the 
metric will have to be Ricci flat. In order to deal with general 
Kahler-Einstein metrics, we found that spin^c is good framework and use 
it to prove the metric stability of Kahler-Einstein metrics with nonpositive 
scalar curvature. As with our previous work, we can use it to draw 
interesting consequences including a (local) volume comparison theorem 
for scalar curvature. This is joint work with Xiaodong Wang and Guofang