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dc.contributor.author
Rivière, Tristan
dc.date.accessioned
2017-06-09T18:12:33Z
dc.date.available
2017-06-09T18:12:33Z
dc.date.issued
2010-07-08
dc.identifier.uri
http://hdl.handle.net/20.500.11850/43457
dc.description.abstract
In this work we present new tools for studying the variations of the Willmore functional of immersed surfaces into Rm. This approach gives for instance a new proof of the existence of a Willmore minimizing embedding of an arbitrary closed surface in arbitrary codimension. We explain how the same approach can solve constraint minimization problems for the Willmore functional. We show in particular that, for a given closed surface and a given conformal class for this surface, there is an immersion in Rm, away possibly from isolated branched points, which minimizes the Willmore energy among all possible Lipschitz immersions in Rm having an L2−bounded second fundamental form and realizing this conformal class. This branched immersion is either a smooth Conformal Willmore branched immersion or an isothermic branched immersion. We show that branched points do not exist whenever the minimal energy in the conformal class is less than 8! and that these immersions extend to smooth conformal Willmore embeddings or global isothermic embeddings of the surface in that case. Finally, as a by-product of our analysis, we establish that inside a compact subspace of the moduli space the following holds : weak limit of Palais Smale Willmore sequences are Conformal Willmore, that weak limits of Palais Smale sequences of Conformal Willmore are either Conformal Willmore or Global Isothermic and finally we observe also that weakly converging Palais Smale sequences of Global Isothermic Immersions are Global Isothermic. The analysis developped along the paper - in particular these last results - opens the door to the possibility of constructing new critical saddle points of the Willmore functional without or with constraints using min max methods.
dc.language.iso
en
dc.title
Variational Principles for immersed Surfaces with L2-bounded Second Fundamental Form
dc.type
Working Paper
ethz.pages.start
arXiv:1007.2997
ethz.size
54 p.
ethz.notes
Submitted on 18 July 2010.
ethz.publication.status
published
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03600 - Rivière, Tristan / Rivière, Tristan
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03600 - Rivière, Tristan / Rivière, Tristan
ethz.identifier.url
http://arxiv.org/abs/1007.2997
ethz.date.deposited
2017-06-09T18:13:02Z
ethz.source
ECIT
ethz.identifier.importid
imp59364ecac7ce556410
ethz.ecitpid
pub:72041
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-12T13:35:29Z
ethz.rosetta.lastUpdated
2018-10-01T15:05:17Z
ethz.rosetta.versionExported
true
ethz.COinS
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