4 papers
Null Geodesics and Improved Unique Continuation for Waves in Asymptotically Anti-de Sitter Spacetimes
Alex McGill, Arick Shao
We consider the question of whether solutions of Klein--Gordon equations on asymptotically Anti-de Sitter spacetimes can be uniquely continued from the conformal boundary. Positive…
The Near-Boundary Geometry of Einstein-Vacuum Asymptotically Anti-de Sitter Spacetimes
Arick Shao
We study the geometry of a general class of vacuum asymptotically Anti-de Sitter spacetimes near the conformal boundary. In particular, the spacetime is only assumed to have finite…
Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials
Alberto Enciso, Arick Shao, Bruno Vergara
We establish a new family of Carleman inequalities for wave operators on cylindrical spacetime domains containing a potential that is critically singular, diverging as an inverse s…
On Carleman and Observability Estimates for Wave Equations on Time-Dependent Domains
Arick Shao
We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main fea…