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Min-max constructions of 2d-minimal surfaces


Pellandini, Filippo Maria Livio. Min-max constructions of 2d-minimal surfaces. 2010, University of Zurich, Faculty of Science.

Abstract

In this thesis we will present a proof of the existence of closed embedded minimal surfaces in a closed 3-dimensional manifold constructed via min-max arguments and we will prove genus bounds for the produced surfaces. A stronger estimate was announced by Pitts and Rubinstein but to our knowledge its proof has never been published. Our proof follows ideas of Simon and uses an extension of a famous result of Meeks, Simon and Yau on the convergence of minimizing sequences of isotopic surfaces.



Eine Minimalfläche ist eine Fläche im Raum, die lokal minimalen Flächeninhalt hat. In dieser Doktorarbeit studiere ich ähnlichen Probleme nicht in Raum, sondern zum Beispiel in einer 3-dimensionale Sphere. Es wird gezeigt, dass 2-dimensionale minimale Flächen in einer 3-Sphere existieren. Danach analysiere ich deren Geometrie.

Abstract

In this thesis we will present a proof of the existence of closed embedded minimal surfaces in a closed 3-dimensional manifold constructed via min-max arguments and we will prove genus bounds for the produced surfaces. A stronger estimate was announced by Pitts and Rubinstein but to our knowledge its proof has never been published. Our proof follows ideas of Simon and uses an extension of a famous result of Meeks, Simon and Yau on the convergence of minimizing sequences of isotopic surfaces.



Eine Minimalfläche ist eine Fläche im Raum, die lokal minimalen Flächeninhalt hat. In dieser Doktorarbeit studiere ich ähnlichen Probleme nicht in Raum, sondern zum Beispiel in einer 3-dimensionale Sphere. Es wird gezeigt, dass 2-dimensionale minimale Flächen in einer 3-Sphere existieren. Danach analysiere ich deren Geometrie.

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Additional indexing

Item Type:Dissertation (monographical)
Referees:De Lellis Camillo, Kappeler Thomas
Communities & Collections:07 Faculty of Science > Institute of Mathematics
UZH Dissertations
Dewey Decimal Classification:510 Mathematics
Language:English
Place of Publication:Zürich
Date:2010
Deposited On:19 Jan 2011 14:21
Last Modified:24 Sep 2019 17:15
Publisher:s.n.
Number of Pages:91
Additional Information:Min-max constructions of 2d-minimal surfaces / vorgelegt von Filippo Maria Livio Pellandini. - Zürich, 2010
OA Status:Green
Related URLs:https://www.recherche-portal.ch/primo-explore/fulldisplay?docid=ebi01_prod006131126&context=L&vid=ZAD&search_scope=default_scope&tab=default_tab&lang=de_DE (Library Catalogue)

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