Control for Schrödinger equation on hyperbolic surfaces

We show that 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 [11–13]. The proof is based on the main estimate in [10] and standard arguments in control theory.

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Received 19 December 2017

Accepted 19 June 2018

Published 25 March 2019