# Nonclassical minimizing surfaces with smooth boundary

created by dephilipp on 22 Jun 2019
modified by delellis on 01 Dec 2020

[BibTeX]

Accepted Paper

Inserted: 22 jun 2019
Last Updated: 1 dec 2020

Journal: J. Differential Geom.
Year: 2019

ArXiv: 1906.09488 PDF

Abstract:

We construct a Riemannian metric $g$ on $\mathbb{R}^4$ (arbitrarily close to the euclidean one) and a smooth simple closed curve $\Gamma\subset \mathbb R^4$ such that the unique area minimizing surface spanned by $\Gamma$ has infinite topology. Furthermore the metric is almost Kahler and the area minimizing surface is calibrated.