We construct a Riemannian metric g on R4(arbitrarily close to the euclidean one) and a smooth simple closed curve Γ ⊂ R4such that the unique area minimizing surface spanned by Γ has infinite topology. Furthermore the metric is almost Kähler and the area minimizing surface is calibrated.
Nonclassical minimizing surfaces with smooth boundary / De Lellis, C.; De Philippis, G.; Hirsch, J.. - In: JOURNAL OF DIFFERENTIAL GEOMETRY. - ISSN 0022-040X. - 122:2(2022), pp. 205-222. [10.4310/JDG/1669998183]
Nonclassical minimizing surfaces with smooth boundary
De Lellis C.;De Philippis G.;
2022-01-01
Abstract
We construct a Riemannian metric g on R4(arbitrarily close to the euclidean one) and a smooth simple closed curve Γ ⊂ R4such that the unique area minimizing surface spanned by Γ has infinite topology. Furthermore the metric is almost Kähler and the area minimizing surface is calibrated.File in questo prodotto:
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