A lower bound for the remainder in Weyl's law on negatively curved surfaces
Spectral Theory
2011-11-09 v3 Differential Geometry
Dynamical Systems
Abstract
We obtain an estimate from below for the remainder in Weyl's law on negatively curved surfaces. In the constant curvature case, such a bound was proved independently by Hejhal and Randol in 1976 using the Selberg zeta function techniques. Our approach works in arbitrary negative curvature, and is based on wave trace asymptotics for long times, equidistribution of closed geodesics and small-scale microlocalization.
Keywords
Cite
@article{arxiv.math/0612250,
title = {A lower bound for the remainder in Weyl's law on negatively curved surfaces},
author = {Dmitry Jakobson and Iosif Polterovich and John A. Toth},
journal= {arXiv preprint arXiv:math/0612250},
year = {2011}
}
Comments
27 pages; section 3 significantly revised. To appear in IMRN