Mathematical Research Letters

Volume 25 (2018)

Number 6

Control for Schrödinger equation on hyperbolic surfaces

Pages: 1865 – 1877



Long Jin (Yau Mathematical Science Center, Tsinghua University, Beijing, China)


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.

Received 19 December 2017

Accepted 19 June 2018

Published 25 March 2019