Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Sergio Almaraz, Universidade Federal Fluminense, Brazil
Inviter:	孙黎明
Title:	Rigidity of non-compact static domains in hyperbolic space via positive mass theorems
Language:	English
Time & Venue:	2023.03.27 10:30-11:30 思源楼S713
Abstract:	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).