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Geometric and spectral properties of compact Riemann orbisurfaces.

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Call No.	Ph.D. 2004
Author	Dryden, Emily B.
Title	Geometric and spectral properties of compact Riemann orbisurfaces.
Date	2004
Abstract	Historically, inverse spectral theory has been concerned with the relationship between the geometry and the spectrum of compact Riemannian manifolds, where spectrum means the eigenvalue spectrum of the Laplace operator as it acts on smooth functions on a manifold M. We examine this relationship in the non-smooth setting, that is, for manifolds which have singularities. We generalize several relevant geometric tools to the setting of cone-surfaces in joint work with Hugo Parlier, we exhibit a collar theorem and a Bers' theorem for cone-surfaces. We describe all cone-surfaces of fixed signature in terms of an underlying combinatorial skeleton and Fenchel-Nielsen parameters. On the spectral side, we give a partial extension of Huber's theorem to Riemann orbisurfaces and use this to show that there are at most finitely many Riemannian orbifolds with the same Laplace spectrum as a given Riemann orbisurface.
Description	vii, 90 leaves : ill. 28 cm.
Format	application/pdf
Advisor	Carolyn S. Gordon.
Subject	Riemannian manifolds. Singularities (Mathematics). Laplacian operator. Spectral theory (Mathematics). Riemann surfaces. Curves on surfaces. Geometry
College	Dartmouth College -- Department of Mathematics.
Issuing Body	Dartmouth Dissertations are made available through the Dartmouth Digital Library.
Degree	Thesis (Ph.D.)--Dartmouth College.
Copyright	All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means without permission in writing from the author.
DOI	http://dx.doi.org/10.1349/ddlp.58

Title	Page 1
Format	application/pdf
Issuing Body	Dartmouth Dissertations are made available through the Dartmouth Digital Library.
Degree	Thesis (Ph.D.)--Dartmouth College.
Full Text	Geometric and Spectral Properties of Compact Riemann Orbisurfaces A Thesis Submitted to the Faculty in partial ful llment of the requirements for the degree of Doctor of Philosophy in Mathematics by Emily B. Dryden DARTMOUTH COLLEGE Hanover, New Hampshire May 24th, 2004 Examining Committee: (chair) Carolyn S. Gordon Eran Makover Scott D. Pauls David L. Webb Carol L. Folt Dean of Graduate Students

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