English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Isoresonant conformal surfaces with cusps and boundedness of the relative determinant

Aldana, C. L. (2010). Isoresonant conformal surfaces with cusps and boundedness of the relative determinant. Communications in Analysis and Geometry, 18(5), 1009-1048. Retrieved from http://arxiv.org/abs/1005.3397.

Item is

Basic

show hide
Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-B078-A Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-B079-8
Genre: Journal Article

Files

show Files
hide Files
:
1005.3397 (Preprint), 339KB
Name:
1005.3397
Description:
File downloaded from arXiv at 2013-02-18 09:41
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
:
CAG-18-5-A6-Aldana.pdf (Any fulltext), 298KB
Name:
CAG-18-5-A6-Aldana.pdf
Description:
-
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
-

Locators

show

Creators

show
hide
 Creators:
Aldana, Clara Lucia1, Author              
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

Content

show
hide
Free keywords: Mathematics, Spectral Theory, math.SP,
 Abstract: We study the isoresonance problem on non-compact surfaces of finite area that are hyperbolic outside a compact set. Inverse resonance problems correspond to inverse spectral problems in the non-compact setting. We consider a conformal class of surfaces with hyperbolic cusps where the deformation takes place inside a fixed compact set. Inside this compactly supported conformal class we consider isoresonant metrics, i.e. metrics for which the set of resonances is the same, including multiplicities. We prove that sets of isoresonant metrics inside the conformal class are sequentially compact. We use relative determinants, splitting formulae for determinants and the result of B. Osgood, R. Phillips and P. Sarnak about compactness of sets of isospectral metrics on closed surfaces. In the second part, we study the relative determinant of the Laplace operator on a hyperbolic surface as function on the moduli space. We consider the moduli space of hyperbolic surfaces of fixed genus and fixed number of cusps. We consider the relative determinant of the Laplace operator and a model operator defined on the cusps. We prove that the relative determinant tends to zero as one approaches the boundary of the moduli space.

Details

show
hide
Language(s):
 Dates: 2010-05-192011-06-132010
 Publication Status: Published in print
 Pages: This is the latest version of the paper, very similar to the published version. Section 3 was reorganized to make it more clear. The paper is based on the second part of my doctoral thesis
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1005.3397
URI: http://arxiv.org/abs/1005.3397
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Communications in Analysis and Geometry
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: Hong Kong : International Press
Pages: - Volume / Issue: 18 (5) Sequence Number: - Start / End Page: 1009 - 1048 Identifier: ISSN: 1019-8385
CoNE: /journals/resource/954925586286