A geometric Ginzburg-Landau problem

Reference:

Moser, R., 2013. A geometric Ginzburg-Landau problem. Mathematische Zeitschrift, 273 (3-4), pp. 771-792.

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Official URL:

http://dx.doi.org/10.1007/s00209-012-1029-5

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.

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