非线性分析研讨班：Rigidity of non-compact static domains in hyperbolic space via positive mass theorems

中科院数学与系统科学研究院

数学研究所

学术报告

非线性分析研讨班

报告人：Sergio Almaraz (Universidade Federal Fluminense, Brazil)

题  目：Rigidity of non-compact static domains in hyperbolic space via positive mass theorems

时  间：2023.03.27（星期一）10:30-11:30

地  点：思源楼S713

摘  要：We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at infinity on any of these latter examples, we formulate and prove a positive mass theorem in the spin category under natural dominant energy conditions (both in the interior and along the boundary) whose rigidity statement retrieves, among other things, a sharper version of a recent result by Souam to the effect that no such hypersurface admits a compactly supported deformation keeping the original lower bound on the mean curvature. A key ingredient in our approach is the consideration of a family of elliptic boundary conditions on spinors interpolating between chirality and MIT bag boundary conditions.  This is a joint work with Levi de Lima (Universidade Federal do Ceará, Brazil).