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The Ricci flow on manifolds with boundary

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dc.contributor.advisor Anderson, Michael en_US
dc.contributor.author Gianniotis, Panagiotis en_US
dc.contributor.other Department of Mathematics en_US
dc.date.accessioned 2017-09-20T16:50:09Z
dc.date.available 2017-09-20T16:50:09Z
dc.date.issued 2013-12-01
dc.identifier.uri http://hdl.handle.net/11401/76395 en_US
dc.description 84 pgs en_US
dc.description.abstract In this thesis, we investigate issues related to boundary value problems for the Ricci flow. First, we focus on a compact manifold with boundary and show the short-time existence, regularity and uniqueness of the flow. To obtain these results we impose the boundary conditions proposed by Anderson for the Einstein equations, namely the mean curvature and the conformal class of the boundary. We also show that a certain continuation principle holds. Our methods still apply when the manifold is not compact, as long as it has compact boundary and an appropriate control of the geometry at infinity. Secondly, motivated by the static extension conjecture in Mathematical General Relativity, we study a boundary value problem for the Ricci flow on warped products. We impose the boundary data proposed by Bartnik for the static vacuum equations, which are the mean curvature and the induced metric of the boundary of the base manifold. We conclude the thesis applying the results above to study the flow on a 3-manifold with symmetry. We show the long time existence of the flow and study its behavior in different situations. 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 boundary, ricci flow en_US
dc.title The Ricci flow on manifolds with boundary en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Khuri, Marcus en_US
dc.contributor.committeemember Chen, Xiu-Xiong en_US
dc.contributor.committeemember Rocek, Martin en_US

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