Surgery for extended Ricci flow systems

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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
Parabolische partielle Differentialgleichungen
Parabolic partial differential equations
Ricci flow
License: Publishing license including print on demand
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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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