Speakers:
Lan-Hsuan Huang (University of Connecticut)
Damin Wu (University of Connecticut)

 

 

Title: 1. Constraint manifolds with the dominant energy condition

 

Abstract:

The deformation results to the strict dominant energy condition are important analytic tools to study the space of initial data sets for the Einstein field equations. For non-vacuum initial data sets, there is a serious technical detail in deforming to the strict inequality from a weak inequality. In the joint work with Justin Corvino, we introduce a new modified Einstein constraint operator. By establishing local surjectivity of the operator, we can promote the dominant energy condition by compactly supported deformations and obtain new gluing results.

 

Title: 2. Holomorphic curvature and canonical metic

 

Abstract:

I will talk about a construction of Kahler-Einstein metric under the assumption of negative holomorphic sectional curvature, based on a joint work with Yau.