A lower bound for the $\Theta$ function on manifolds without conjugate points
Differential Geometry
2017-09-15 v1 Spectral Theory
Abstract
In this short note, we prove that the usual function on a Riemannian manifold without conjugate points is uniformly bounded from below. This extends a result of Green in two dimensions. This elementary lemma implies that the B\'erard remainder in the Weyl law is valid for a manifold without conjugate points, without any restriction on the dimension.
Keywords
Cite
@article{arxiv.1603.05697,
title = {A lower bound for the $\Theta$ function on manifolds without conjugate points},
author = {Yannick Bonthonneau},
journal= {arXiv preprint arXiv:1603.05697},
year = {2017}
}