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 Philippis G.;
2022
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.
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