Control for Schrödinger equation on hyperbolic surfaces

2017/07/17 by Long Jin, Jin, Long · 4 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1707.04990

openalex publication_date 2017/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the any nonempty open set on a hyperbolic surface provides observability and control for the time dependent Schrödinger equation. The only other manifolds for which this was previously known are flat tori. The proof is based on the main estimate in Dyatlov-Jin and standard arguments of control theory.

Citations

• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• Rough controls for Schroedinger operators on 2-tori
• Dispersion and controllability for the Schrödinger equation on negatively curved manifolds

Cited by

• Observable sets for the free Schrödinger equation on combinatorial graphs
• Observability estimates for the Schrödinger equation on the equilateral triangle
• Observability of Schrödinger propagators on tori in rough settings
• Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus

Related

• Controllability of the Schrödinger equation on unbounded domains without geometric control condition
• Control for Schrödinger equations on 2-tori: rough potentials
• Control for Schroedinger operators on tori
• Control From an Interior Hypersurface
• Resolvent bounds imply observability from measurable time sets for Schrödinger equations