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Min-max constructions of 2d-minimal surfaces


Pellandini, F M. Min-max constructions of 2d-minimal surfaces. 2010, University of Zurich, Faculty of Science.

Abstract

In this thesis we will present (following [CDL03]) the 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.

Abstract

In this thesis we will present (following [CDL03]) the 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.

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Additional indexing

Item Type:Dissertation (monographical)
Referees:De Lellis C, Kappeler T
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2010
Deposited On:19 Jan 2011 14:21
Last Modified:23 Nov 2018 20:56
Number of Pages:88
Additional Information:Min-max constructions of 2d-minimal surfaces / vorgelegt von Filippo Maria Livio Pellandini. - Zürich, 2010
OA Status:Green
Related URLs:http://opac.nebis.ch/F/?local_base=NEBIS&con_lng=GER&func=find-b&find_code=SYS&request=006131126

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