A geometric Ginzburg-Landau problem

Roger Moser

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/0878a730-e143-43ca-acc8-617456191b6c • DOI: https://doi.org/10.1007/s00209-012-1029-5

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.