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arXiv · 1906.09488

Nonclassical minimizing surfaces with smooth boundary

Camillo De Lellis·Guido De Philippis·Jonas Hirsch
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Abstract

We construct a Riemannian metric $g$ on $\mathbb{R}^4$ (arbitrarily close to the euclidean one) and a smooth simple closed curve $Γ\subset \mathbb R^4$ such 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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Camillo De Lellis, Guido De Philippis, Jonas Hirsch. 2019-06-29. Nonclassical minimizing surfaces with smooth boundary. https://arxiv.org/abs/1906.09488

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