Mathematical Research Letters

Volume 27 (2020)

Number 2

Finiteness of small eigenvalues of geometrically finite rank one locally symmetric manifolds

Pages: 465 – 500

DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n2.a6

Author

Jialun Li (Institut de Mathématiques de Bordeaux, Universit´e de Bordeaux, Talence, France)

Abstract

Let $M$ be a geometrically finite rank one locally symmetric manifolds. We prove that the spectrum of the Laplace operator on $M$ is finite in a small interval which is optimal.

Received 6 September 2018

Accepted 11 March 2019

Published 8 June 2020