This research concerns three areas of spectral geometry: (1) spectral geometry, trace formulas, and determinants for Kleinian groups, (2) finiteness and compactness theorems for isopectral Riemannian manifolds, and (3) spectral geometry of free boundary problems. The research concerns the development of trace formulas and the study of determinants of Laplacians for arbitrary geometrically finite discrete groups of hyperbolic isometries. The emphasis is on co-infinite volume groups, and the goal is to understand poles of the scattering operator geometrically and to study the behavior of the determinant of the Laplacian and Selberg zeta function under deformations. This research is in the general area of geometry and, in particular, Kleinian groups acting on hyperbolic n-dimensional space. The research has significance both to geometry and to mathematical physics.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
9203529
Program Officer
James Glazebrook
Project Start
Project End
Budget Start
1992-06-01
Budget End
1996-05-31
Support Year
Fiscal Year
1992
Total Cost
$123,000
Indirect Cost
Name
University of Kentucky
Department
Type
DUNS #
City
Lexington
State
KY
Country
United States
Zip Code
40506