Constant Q-Curvature Metrics Near the Hyperbolic Metric

Doctoral Dissertation

Abstract

Let (M, g) be a Poincaré-Einstein manifold with a smooth defining function. We prove that there are infinitely many asymptotically hyperbolic metrics with constant Q-curvature in the conformal class of an asymptotically hyperbolic metric close enough to g. These metrics are parametrized by the elements in the kernel of the linearized operator of the prescribed constant Q-curvature equation. A similar analysis is applied to a class of fourth order equations arising in spectral theory.

Attributes

Attribute NameValues
URN
  • etd-04162013-194310

Author Gang Li
Advisor Matthew Gursky
Contributor Matthew Gursky, Committee Chair
Contributor Frederico Xavier, Committee Member
Contributor Gabor Szekelyhidi, Committee Member
Contributor Xiaobo Liu, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2013-03-26

Submission Date 2013-04-16
Country
  • United States of America

Subject
  • Fredholm property

  • perturbation problem

  • inverse function theorem

  • edge operator

  • asymptotically hyperbolic manifolds

  • Fourth order semilinear elliptic equations

  • constant $Q$-curvature metric

  • degenerate operators

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility Public
Content License
  • All rights reserved

Departments and Units

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