Noether's Theorem and the Willmore Functional
Yann Bernard
TL;DR
This paper applies Noether's theorem to the Willmore functional to derive conservation laws for its critical points, recovering previous results and providing detailed examples.
Contribution
It introduces a novel application of Noether's theorem to the Willmore functional, deriving new conservation laws and unifying previous findings.
Findings
Derived conservation laws for Willmore critical points
Recovered previous results by Capovilla, Guven, and Riviere
Provided detailed examples illustrating the theory
Abstract
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. Riviere. Several examples are considered in details.
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