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Constant Q-Curvature Metrics Near the Hyperbolic Metric

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posted on 2013-04-16, 00:00 authored by Gang Li
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.

History

Date Modified

2017-06-02

Defense Date

2013-03-26

Research Director(s)

Matthew Gursky

Committee Members

Frederico Xavier Gabor Szekelyhidi Xiaobo Liu

Degree

  • Doctor of Philosophy

Degree Level

  • Doctoral Dissertation

Language

  • English

Alternate Identifier

etd-04162013-194310

Publisher

University of Notre Dame

Program Name

  • Mathematics

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