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dc.contributor.advisor Forman, Robin
dc.creatorRichardson, Ken
dc.date.accessioned 2009-06-04T00:38:34Z
dc.date.available 2009-06-04T00:38:34Z
dc.date.issued 1993
dc.identifier.urihttps://hdl.handle.net/1911/16660
dc.description.abstract The determinant of the Laplace operator, det $\Delta$, is a function on the set of metrics on a compact manifold. Generalizing the work of Osgood, Phillips, and Sarnak on surfaces, we consider one-parameter variations of metrics of fixed volume in the conformal class of a given metric. By calculating the derivative of $-$log(det $\Delta$) with respect to such variations, we find the condition for a metric to be a critical point of the determinant function. Homogeneous manifolds satisfy this condition, but we exhibit examples of locally homogeneous manifolds which are not critical points in dimensions $\ge$3. For 3-dimensional manifolds, we derive a formula for the second derivative of $-$log(det $\Delta$) with respect to such a variation, at a critical point. Using this formula, we show that the standard metric on the sphere $S\sp3$ is a local maximum of the determinant function.
dc.format.extent 58 p.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
dc.title Critical points of the determinant of the Laplace operator
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Mathematics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy
dc.identifier.citation Richardson, Ken. "Critical points of the determinant of the Laplace operator." (1993) Diss., Rice University. https://hdl.handle.net/1911/16660.


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