A geometric Ginzburg-Landau problem

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Abstract

For surfaces embedded in a three-dimensional Euclidean space, consider a functional consisting of two terms: a version of the Willmore energy and an anisotropic area penalising the first component of the normal vector, the latter weighted with the factor 1/epsilon^2. The asymptotic behaviour of such functionals as epsilon tends to 0 is studied in this paper. The results include a lower and an upper bound on the minimal energy subject to suitable constraints. Moreover, for embedded spheres, a compactness result is obtained under appropriate energy bounds.
Original languageEnglish
Pages (from-to)771-792
Number of pages22
JournalMathematische Zeitschrift
Volume273
Issue number3-4
Early online date11 Apr 2012
DOIs
Publication statusPublished - Apr 2013

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