Open Access
March 2013 Minimizers of the Willmore functional under fixed conformal class
Ernst Kuwert , Reiner Schätzle
J. Differential Geom. 93(3): 471-530 (March 2013). DOI: 10.4310/jdg/1361844942


We prove the existence of a smooth minimizer of the Willmore energy in the class of conformal immersions of a given closed Riemann surface into $\mathbb{R}^n, n = 3, 4$, if there is one conformal immersion with Willmore energy smaller than a certain bound $\mathcal{W}_{n,p}$ depending on codimension and genus $p$ of the Riemann surface. For tori in codimension 1, we know $\mathcal{W}_{3,1} = 8\pi$.


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Ernst Kuwert . Reiner Schätzle. "Minimizers of the Willmore functional under fixed conformal class." J. Differential Geom. 93 (3) 471 - 530, March 2013.


Published: March 2013
First available in Project Euclid: 26 February 2013

zbMATH: 1276.53010
MathSciNet: MR3024303
Digital Object Identifier: 10.4310/jdg/1361844942

Rights: Copyright © 2013 Lehigh University

Vol.93 • No. 3 • March 2013
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