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dc.contributor.advisorGang Tian.en_US
dc.contributor.authorŠešum, Nataša, 1975-en_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.date.accessioned2006-03-29T18:27:14Z
dc.date.available2006-03-29T18:27:14Z
dc.date.copyright2004en_US
dc.date.issued2004en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/32244
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.en_US
dc.descriptionIncludes bibliographical references (p. 83-85).en_US
dc.description.abstractConsider the unnormalized Ricci flow ...Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times ... then the solution can be extended beyond T. In the thesis we prove that if the Ricci curvature is uniformly bounded under the flow for all times ... then the curvature tensor has to be uniformly bounded as well. In particular, this means that if the Ricci tensor stays uniformly bounded up to a finite time T, a Ricci flow can not develop a singularity at T. We will give two different proofs of that result. One of them relies on Hamilton's estimates on distance changes along the flow and the other one relies on the identities for reduced distances and the monotonicity formula for reduced volumes that has been introduced and proved by Perelman in [29]. Consider the Ricci flow ... on a closed, n-dimensional manifold M. Assume that a solution of the flow exists for all times ... and that the curvatures and the diameters are uniformly bounded along the flow. We will prove that for every sequence ... there exists a subsequence such that g(ti + t) converges to a metric h(t) and h(t) is a Ricci soliton. We will also prove that if one of the limit solitons is integrable, then a soliton that we get in the limit is unique up to diffeomorphisms and the convergence toward it is exponential.en_US
dc.description.abstract(cont.) We will also prove that in an arbitrary dimension, for a given Kähler-Ricci flow with uniformly bounded Ricci curvatures, for every sequence of times ti converging to infinity, there exists a subsequence such that ... and the convergence is smooth outside a singular set (which is a set of codimension at least 4). Moreover, g(t) is a solution of the flow off the singular set. In the case of a complex dimension 2, for any sequence of times converging to infinity we can find a subsequence of times such that we have a convergence toward a Kähler-Ricci soliton, away from finitely many isolated singularities.en_US
dc.description.statementofresponsibilityby Nataša Šešum.en_US
dc.format.extent85 p.en_US
dc.format.extent3317393 bytes
dc.format.extent3315585 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582
dc.subjectMathematics.en_US
dc.titleLimiting behavior of Ricci flowsen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Dept. of Mathematics.en_US
dc.identifier.oclc56019708en_US


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