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

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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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