Thep-spectrum of the Laplacian on compact hyperbolic three manifolds.

Title: Thep-spectrum of the Laplacian on compact hyperbolic three manifolds.
Identifier: AAI9224837
identifier: 9224837
Creator: McGowan, Jeffrey Kirk.
Contributor: Adviser: Jozef Dodziuk
Date: 1992
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: In this paper we will study the spectrum of the Laplacian acting on differential forms on compact three dimensional manifolds of constant curvature {dollar}-{dollar}1. In particular, given a non-compact manifold M with Vol(M) = V, and a sequence of compact M{dollar}\sb{lcub}\rm i{rcub}{dollar} approaching M, we show that there are many small eigenvalues, and give an upper bound on the rate at which they can accumulate at 0. More precisely, we show that the number of eigenvalues of the Laplacian on forms of degree one in the interval (0,1/(c{dollar}\sb1{dollar}V(1 + R{dollar}\sp2)){dollar} is less than or equal to c{dollar}\sb2{dollar}V, where R is the diameter of M.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.

Media: Thep-spectrum of the Laplacian on compact hyperbolic three manifolds.