Lower bounds for Cauchy data on curves in a negatively curved surface
Analysis of PDEs
2022-06-14 v1 Mathematical Physics
math.MP
Abstract
We prove a uniform lower bound on Cauchy data on an arbitrary curve on a negatively curved surface using the Dyatlov-Jin(-Nonnenmacher) observability estimate on the global surface. In the process, we prove some further results about defect measures of restrictions of eigenfunctions to a hypersurface.
Cite
@article{arxiv.2002.09456,
title = {Lower bounds for Cauchy data on curves in a negatively curved surface},
author = {Jeffrey Galkowski and Steve Zelditch},
journal= {arXiv preprint arXiv:2002.09456},
year = {2022}
}