Control of eigenfunctions on hyperbolic surfaces: an application of fractal uncertainty principle
Analysis of PDEs
2017-10-25 v1 Classical Analysis and ODEs
Dynamical Systems
Spectral Theory
Chaotic Dynamics
Abstract
This expository article, written for the proceedings of the Journ\'ees EDP (Roscoff, June 2017), presents recent work joint with Jean Bourgain [arXiv:1612.09040] and Long Jin [arXiv:1705.05019]. We in particular show that eigenfunctions of the Laplacian on hyperbolic surfaces are bounded from below in norm on each nonempty open set, by a constant depending on the set but not on the eigenvalue.
Keywords
Cite
@article{arxiv.1710.08762,
title = {Control of eigenfunctions on hyperbolic surfaces: an application of fractal uncertainty principle},
author = {Semyon Dyatlov},
journal= {arXiv preprint arXiv:1710.08762},
year = {2017}
}
Comments
18 pages