Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.773921
Title: Aspects of pseudolocality in Ricci flow
Author: McLeod, Andrew Donald
ISNI:       0000 0004 7961 1540
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2018
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Abstract:
This thesis explores two separate problems related to the phenomenon of pseudolocality within Ricci flow. First, we consider the regularity of noncollapsed three-dimensional Ricci limit spaces via Ricci flow. We introduce a new weakened notion of Ricci flow, termed Pyramid Ricci flow, and use it to establish that a noncollapsed three-dimensional Ricci limit space is homeomorphic to a smooth manifold via a globally-defined homeomorphism that is bi-Hӧlder once restricted to any compact subset. We include the full details of a well-known compactness result which this work relies upon. Second, we consider the pseudolocality phenomenon in an almost-hyperbolic setting. We obtain an improved pseudolocality result for Ricci flows on two-dimensional surfaces that are initially almost-hyperbolic on large hyperbolic balls. We prove that, at the central point of the hyperbolic ball, the Gauss curvature remains close to the hyperbolic value for a time that grows exponentially in the radius of the ball. This two-dimensional result allows us to precisely conjecture how the phenomenon should appear in the higher dimensional setting.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.773921  DOI: Not available
Keywords: QA Mathematics
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