The action of the Ricci flow on almost flat manifolds [Elektronische Ressource] / vorgelegt von Galina Guzhvina

Description

Guzhvina Galina.The Action of the Ricci Flow on Almost Flat Manifolds.2007Reine MathematikThe Action of the Ricci Flow on Almost Flat Manifolds.Inaugural-Dissertation zur Erlangung des Doktorgrades derNaturwissenschaften im Fachbereich Mathematik und Informatik derMathematisch-Naturwissenschaftlichen Fakult atder Westf alischen Wilhelms-Universit at Mnstervorgelegt vonGalina Guzhvina2007 Dekan: Prof. Dr. Joachim Cuntz Erster Gutachter: Prof. Dr. Burkard Wilking Zweiter Gutachter: Prof. Dr. Christoph Böhm Tag der mündlichen Prüfung: 09.07.2007 Tag der Promotion: 5AbstractThe present work studies how the Ricci flow acts on almost flat manifolds. WeshowthattheRicciflowexistsonany"-flatRiemannianmanifold(M;g)with"small2enough for any t 2 R ; that lim jKj ¢diam (M;g ) = 0 along the Ricci‚0 t!1 t(M;g )tflow and in the case when the fundamental group of (M;g ) is (almost) Abelian wet0obtaintheC -convergenceofthemetrictoaflatlimitmetric. Thecasesof… (M;g )1 tAbelianandnon-Abelianarehandledintwodifferentways. Apartfromthatwegiveexamples that show that the pinching constant in the Gromov’s theorem necessarilydepends on the dimension of the manifold.6ContentsAcknowledgments. 9Introduction 111 Ricci Flow on Almost Flat Manifolds. Abelian Case. 191.1 Short Geodesic Loops. General Information. . . . . . . . . . . . . . 201.

Sujets

• Mathematics

Informations

• Publié par: westfalische_wilhelms-universitat_munster
• Publié le: 01 janvier 2007
• Nombre de lectures: 30
• Langue: English

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The

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Guzhvina

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Galina.

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2007

Almost

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Manifolds.

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Erster Gutachter:

Zweiter Gutachter:

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Tag der mündlichen Prüfung:

Tag der Promotion:

Prof. Dr. Joachim Cuntz

Prof. Dr. Burkard Wilking

Prof. Dr. Christoph Böhm

09.07.2007

09.07.2007