Perez-AyalaS042021D.pdf (545.31 kB)
Extremal Eigenvalues for Conformally Covariant Operators
thesis
posted on 2021-04-13, 00:00 authored by Samuel Pérez-AyalaRiemannian metrics that extremize eigenvalues of conformally covariant operators are known to have a relationship with the existence of solutions of important partial differential equations (PDEs). On compact surfaces with no boundary, the study of such extremal metrics for the Laplace-Beltrami operator has led mathematicians to special examples of minimal surfaces and harmonic maps into spheres. This thesis is devoted to the study of the existence and properties of extremal metrics for other natural and geometrically defined differential operators. Questions about the regularity of extremal metrics, possible obstructions to their existence, and to which PDEs are these associated with are discussed.
History
Date Modified
2021-05-20Defense Date
2021-04-08CIP Code
- 27.0101
Research Director(s)
Matthew J. GurskyCommittee Members
Marco Radeschi Qing Han Nicholas EdelenDegree
- Doctor of Philosophy
Degree Level
- Doctoral Dissertation
Language
- English
Alternate Identifier
1250640411Library Record
6022707OCLC Number
1250640411Program Name
- Mathematics
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