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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang

IMPACT FACTOR 2018: 2.316

CiteScore 2018: 1.77

SCImago Journal Rank (SJR) 2018: 2.350
Source Normalized Impact per Paper (SNIP) 2018: 1.465

Mathematical Citation Quotient (MCQ) 2018: 1.44

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Volume 8, Issue 4


New examples of conformally constrained Willmore minimizers of explicit type

Cheikh Birahim Ndiaye / Reiner Michael Schätzle
Published Online: 2014-03-15 | DOI: https://doi.org/10.1515/acv-2014-0005


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-r2S1S3 for r1/2.

Keywords: Willmore surfaces; conformal parametrization

MSC: 53A05; 53A30; 53C21

About the article

Received: 2013-07-23

Revised: 2014-01-22

Accepted: 2014-01-24

Published Online: 2014-03-15

Published in Print: 2015-10-01

Funding Source: DFG

Award identifier / Grant number: TR 71 Freiburg-Tübingen

Citation Information: Advances in Calculus of Variations, Volume 8, Issue 4, Pages 291–319, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2014-0005.

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