Inverse spectral theory and relative determinants of elliptic operators on surfaces with cusps
Inverse spectral theory and relative determinants of elliptic operators on surfaces with cusps
dc.contributor.advisor | Müller, Werner | |
dc.contributor.author | Aldana Domínguez, Clara Lucía | |
dc.date.accessioned | 2020-04-13T21:33:39Z | |
dc.date.available | 2020-04-13T21:33:39Z | |
dc.date.issued | 29.01.2009 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/4026 | |
dc.description.abstract | This thesis concerns relative determinants for Laplacians on surfaces with asymptotically cusps ends and the inverse spectral problem on surfaces with cusps. We consider $(M,g)$, a surface with cusps, and a metric on the surface that is a conformal transformation of the initial metric $h=e^{2\varphi}g$. In the first part we find conditions $\varphi$ that make it possible to define the relative determinant of the pair $(\Delta_{h},\Delta_{g})$. We prove Polyakov's formula for the relative determinant and study the extremal values of this determinant as a function of unit area metrics inside a conformal class. We prove that if the maximum exists it has to be attained at the metric of constant curvature. We discuss necessary conditions for the existence of a maximizer. In the second part we restrict our attention to hyperbolic surfaces of fixed genus and a fixed number of cusps. We study the relative determinant as a function on the moduli space for this kind of surfaces and use the results of J. Jorgenson and R Lundelius in [19] to prove that it tends to zero at the boundary of the moduli space. In the third part we return to general surfaces with cusps. We prove a splitting formula for the relative determinant and use it to prove compactness in the $C^{\infty}$-topology of sets of isospectral metrics in a given conformal class. We assume that the conformal factors $\varphi$ have support in a fixed compact set of $M$. | en |
dc.language.iso | eng | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject.ddc | 510 Mathematik | |
dc.title | Inverse spectral theory and relative determinants of elliptic operators on surfaces with cusps | |
dc.type | Dissertation oder Habilitation | |
dc.publisher.name | Universitäts- und Landesbibliothek Bonn | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.identifier.urn | https://nbn-resolving.org/urn:nbn:de:hbz:5N-16610 | |
ulbbn.pubtype | Erstveröffentlichung | |
ulbbnediss.affiliation.name | Rheinische Friedrich-Wilhelms-Universität Bonn | |
ulbbnediss.affiliation.location | Bonn | |
ulbbnediss.thesis.level | Dissertation | |
ulbbnediss.dissID | 1661 | |
ulbbnediss.date.accepted | 16.01.2009 | |
ulbbnediss.fakultaet | Mathematisch-Naturwissenschaftliche Fakultät | |
dc.contributor.coReferee | Paycha, Sylvie |
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