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 $N#M$.
Connected sum construction of constant Q-curvature manifolds in higher dimensions
Doctoral Dissertation
Abstract
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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 |
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Submission Date | 2014-04-15 |
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Record Visibility | Public |
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LinYJ042014D.pdf | 451 KB | application/pdf | Public |
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