A lower bound for eigenvalue of Laplace operator on locally symmetric space

Abstract

This dissertation is concerned with the lower bound for the first eigenvalue λ1(T) of Laplace operator Δ on a locally symmetric space T \ G / K, where G = SO2n+1(C) with n ≥ 5, T is a lattice in G and K is a maximal compact subgroup of G. It is well known that Casimir operator C acts by a scalar -λπ on each irreducible admissible representation π of G by Diximir's Schur Lemma. We will show that there exists a spectral gap between the greatest lower bound of λ1(T) for those lattices T arising from some imaginary quadratic field and the infimum λ1(G) of λπ, when π passes through all those nontrivial irreducible spherical unitary representation of G.

Date of Award	2010
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology