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International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 35, Issue 2


Local minimizers of the Willmore functional

Florian Skorzinski
  • Arbeitsbereich Analysis, Fachbereich Mathematik, Eberhard-Karls-Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
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Published Online: 2014-04-15 | DOI: https://doi.org/10.1515/anly-2012-1274


Since the Willmore functional is invariant with respect to conformal transformations and reparametrizations, the kernel of the second derivative of the functional at a critical point will always contain a subspace generated by these transformations. We prove that the second derivative being positive definite outside this space is a sufficient condition for a critical point to be a local minimizer.

Keywords: Willmore surfaces; Willmore flow

MSC: 53C42; 35J15; 58B10

About the article

Received: 2014-07-07

Revised: 2015-02-13

Accepted: 2015-02-26

Published Online: 2014-04-15

Published in Print: 2015-05-01

Citation Information: Analysis, Volume 35, Issue 2, Pages 93–115, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1515/anly-2012-1274.

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