New examples of conformally constrained Willmore minimizers of explicit type

Cheikh Birahim Ndiaye; Reiner Michael Schätzle

doi:10.1515/acv-2014-0005

Article

New examples of conformally constrained Willmore minimizers of explicit type

Cheikh Birahim Ndiaye and Reiner Michael Schätzle

Published/Copyright: March 15, 2014

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From the journal Advances in Calculus of Variations Volume 8 Issue 4

Abstract

We develop a convergence procedure to improve weak convergence of conformally constrained Willmore immersions to smooth convergence and apply this to get new examples of conformally constrained Willmore minimizers of explicit type. In fact by estimates of Li–Yau in [Inventiones Mathematicae 69 (1982), 269–291] and Montiel–Ros in [Inventiones Mathematicae 83 (1986), 153–166], the Clifford torus T Cliff =(1/2)(S1×S1)⊆S3 minimizes the Willmore energy in its conformal class. We extend this using our convergence procedure to the flat constant mean curvature tori Tr=rS1×1-r2S1⊆S3 for r≈1/2.

Keywords: Willmore surfaces; conformal parametrization

MSC: 53A05; 53A30; 53C21

Funding source: DFG

Award Identifier / Grant number: TR 71 Freiburg-Tübingen

Received: 2013-7-23

Revised: 2014-1-22

Accepted: 2014-1-24

Published Online: 2014-3-15

Published in Print: 2015-10-1

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Articles in the same Issue

https://doi.org/10.1515/acv-2014-0005

Keywords for this article

Willmore surfaces; conformal parametrization