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NCTS Seminar in Differential Geometry
10:00 - 12:10, July 21, 2016 (Thursday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Title: 1. Constraint Manifolds with the Dominant Energy Condition
Title: 2. Holomorphic Curvature and Canonical Metic
Lan-Hsuan Huang (University of Connecticut)

Lan-Hsuan Huang (University of Connecticut)
Damin Wu (University of Connecticut)
Kuo-Wei Lee (NTU)
Yng-Ing Lee (NTU)
Chun-Chi Lin (NTNU)
Chung-Jun Tsai (NTU)
Mao-Pei Tsui (NTU)
Title: 1. Constraint manifolds with the dominant energy condition

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

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.


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