Connected sum construction of constant Q-curvature manifolds in higher dimensions

Doctoral Dissertation

Abstract

For a compact Riemannian manifold $(M, g2)$ of dimension $ngeq 6$ with constant $Q$-curvature satisfying a nondegeneracy condition, we show that one can construct many other examples of constant $Q$-curvature manifolds by a gluing construction. In this dissertation, we provide a general procedure of gluing together $(M,g2)$ with any compact manifold $(N, g_1)$ satisfying a natural geometric assumption. In particular, we prove the existence of solutions of a fourth-order partial differential equation, which implies the existence of a smooth metric with constant $Q$-curvature on the connected sum $N#M$.

Attributes

Attribute NameValues
URN
  • etd-04152014-181307

Author Yueh-Ju Lin
Advisor Matthew Gursky
Contributor Xiaobo Liu, Committee Member
Contributor Liviu Nicolaescu, Committee Member
Contributor Matthew Gursky, Committee Chair
Contributor Gabor Szekelyhidi, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2014-03-25

Submission Date 2014-04-15
Country
  • United States of America

Subject
  • Q-curvature

  • conformal geometry

  • connected sum

  • Paneitz operator

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility and Access Public
Content License
  • All rights reserved

Departments and Units

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