29 citations · 174 across the 25 of their papers we have counts for
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Bulk-boundary correspondences and unique continuation in asymptotically Anti-de Sitter spacetimes
Arick Shao
This article surveys the research presented by the author at the MATRIX Institute workshop "Hyperbolic Differential Equations in Geometry and Physics" in April 2022. The work is ce…
The bulk-boundary correspondence for the Einstein equations in asymptotically Anti-de Sitter spacetimes
Gustav Holzegel, Arick Shao
In this paper, we consider vacuum asymptotically anti-de Sitter spacetimes with conformal boundary . We establish a corresponden…
A gauge-invariant unique continuation criterion for waves in asymptotically Anti-de Sitter spacetimes
Athanasios Chatzikaleas, Arick Shao
We reconsider the unique continuation property for a general class of tensorial Klein-Gordon equations of the form \begin{align*} \Box_{g} ϕ+ σϕ= \mathcal{G}(ϕ,\nabla ϕ) \text{,} \…
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…
Unique continuation from infinity in asympotically Anti-de Sitter spacetimes II: Non-static boundaries
Gustav Holzegel, Arick Shao
We generalize our unique continuation results recently established for a class of linear and nonlinear wave equations on asymptotically…
Unique continuation from infinity in asymptotically Anti-de Sitter spacetimes
Gustav Holzegel, Arick Shao
We consider the unique continuation properties of asymptotically Anti-de Sitter spacetimes by studying Klein-Gordon-type equations , $σ\…