Noether's theorem and the Willmore functional

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Noether's theorem and the invariances of the Willmore functional are used to derive conservation laws that are satisfied by the critical points of the Willmore energy subject to generic constraints. We recover in particular previous results independently obtained by R. Capovilla and J. Guven, and by T. Rivière. Several examples are considered in detail.

Original languageEnglish
Pages (from-to)217-234
Number of pages18
JournalAdvances in Calculus of Variations
Issue number3
Publication statusPublished - 1 Jul 2016
Externally publishedYes


  • Conservation laws
  • Noether's theorem
  • Willmore functional

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