University of Notre Dame
Browse

Extremal Eigenvalues for Conformally Covariant Operators

Download (545.31 kB)
thesis
posted on 2021-04-13, 00:00 authored by Samuel Pérez-Ayala

Riemannian 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

2021-05-20

Defense Date

2021-04-08

CIP Code

  • 27.0101

Research Director(s)

Matthew J. Gursky

Committee Members

Marco Radeschi Qing Han Nicholas Edelen

Degree

  • Doctor of Philosophy

Degree Level

  • Doctoral Dissertation

Language

  • English

Alternate Identifier

1250640411

Library Record

6022707

OCLC Number

1250640411

Program Name

  • Mathematics

Usage metrics

    Dissertations

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC