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EPSRC Reference: GR/N07448/01
Title: THE SPECTRUM OF THE LAPLACIAN ON HYPERBOLIC 3-MANIFOLDS
Principal Investigator: Anderson, Dr J
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: School of Mathematics
Organisation: University of Southampton
Scheme: Standard Research (Pre-FEC)
Starts: 14 July 2000 Ends: 13 June 2002 Value (£): 7,450
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
The structure of the spectrum of the Laplacian on a geometrically finite hyperbolic 3-manifold is completely understood. In this work, we consider the structure of the Laplacian on geometrically infinite hyperbolic 3-manifolds with finitely generated fundamental group. The ultimate goal of the project is to show that Conjectures C and D in the case for support, which describe the spectrum of the Laplacian on geometrically infinite hyperbolic 3-manifolds, hold. The specific objectives of this project are to consider these conjectures in the test case of geometrically finite hyperbolic 3-manifolds. As it is conjectured that all geometrically infinite hyperbolic 3-manifolds are limits of sequences of geometrically finite hyperbolic 3-manifolds, this project will allow us to develop techniques to handle geometrically infinite Kleinian groups which are limits.
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Organisation Website: http://www.soton.ac.uk