Surgery for extended Ricci flow systems

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URI: http://hdl.handle.net/10900/96423
http://nbn-resolving.de/urn:nbn:de:bsz:21-dspace-964235
http://dx.doi.org/10.15496/publikation-37806
Dokumentart: Dissertation
Date: 2019-12-16
Language: English
Faculty: 7 Mathematisch-Naturwissenschaftliche Fakultät
Department: Mathematik
Advisor: Huisken, Gerhard (Prof. Dr.)
Day of Oral Examination: 2019-11-08
DDC Classifikation: 510 - Mathematics
Keywords: Geometrische Analysis
Other Keywords: Ricci-Fluss
Chirugie
Parabolische partielle Differentialgleichungen
Parabolic partial differential equations
Surgery
Ricci flow
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Abstract:

In this thesis extended Ricci flow systems, which are obtained by coupling Ricci flow to the harmonic map heat flow, are studied. The interest in this system stems from its connection to static solutions to the vacuum Einstein equations and Ricci flow on manifolds with warped product metrics. We prove a convergence theorem and a singularity classification theorem and construct the flow with surgery in the spirit of Hamilton and Perelman for three-dimensional solutions.

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