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# Compactness and Non-compactness for the Yamabe Problem on Manifolds With Boundary

 dc.contributor.advisor Khuri, Marcus A en_US dc.contributor.author Disconzi, Marcelo Mendes en_US dc.contributor.other Department of Mathematics en_US dc.date.accessioned 2013-05-22T17:34:24Z dc.date.accessioned 2015-04-24T14:46:29Z dc.date.available 2013-05-22T17:34:24Z dc.date.available 2015-04-24T14:46:29Z dc.date.issued 2012-05-01 dc.identifier Disconzi_grad.sunysb_0771E_10863 en_US dc.identifier.uri http://hdl.handle.net/1951/59630 en_US dc.identifier.uri http://hdl.handle.net/11401/71203 en_US dc.description 116 pg. en_US dc.description.abstract We study the problem of conformal deformation of Riemannian structure to constant scalar curvature with zero mean curvature on the boundary. We prove compactness for the full set of solutions when the boundary is umbilic and the dimension $n \leq 24$. The Weyl Vanishing Theorem is also established under these hypotheses, and we provide counter-examples to compactness when $n \geq 25$. Lastly, our methods point towards a vanishing theorem for the umbilicity tensor, which is anticipated to be fundamental for a study of the nonumbilic case. en_US dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US dc.format Monograph en_US dc.format.medium Electronic Resource en_US dc.language.iso en_US en_US dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US dc.subject.lcsh Mathematics en_US dc.subject.other Compacness, Manifolds with boundary, Yamabe problem en_US dc.title Compactness and Non-compactness for the Yamabe Problem on Manifolds With Boundary en_US dc.type Dissertation en_US dc.mimetype Application/PDF en_US dc.contributor.committeemember Ebin, David G en_US dc.contributor.committeemember Anderson, Michael T en_US dc.contributor.committeemember Douglas, Michael R. en_US
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