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Localized Deformations and Gluing Constructions in General Relativity

组织者

拉尔斯•安德森 , 赵博文

演讲者

Hongyi Sheng

时间

2024年09月20日 10:30 至 11:30

地点

Online

线上

Zoom 559 700 6085 (BIMSA)

摘要

Gluing constructions of initial data sets play an important role in general relativity. Earlier in 1979, Schoen-Yau used gluing constructions with conformal deformations as a crucial step in their proof of the famous positive mass theorem. Later Corvino modified the gluing constructions with a localized deformations, so that the structure of the manifold near infinity is well-preserved. In this talk, we will review some recent localized deformation theorems and their applications regarding rigidity and non-rigidity type results. We will then see that some results may be generalized to half space with boundary, thanks to our localized deformation techniques near the boundary. On the other hand, for the domains where localized deformation techniques are not valid (called non-generic domains), we will see that they are closely related to certain rigidity theorems.