Calculus of Variations and Geometric Measure Theory

C. De Lellis - G. De Philippis - J. Hirsch

Nonclassical minimizing surfaces with smooth boundary

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


Accepted Paper

Inserted: 22 jun 2019
Last Updated: 1 dec 2020

Journal: J. Differential Geom.
Year: 2019

ArXiv: 1906.09488 PDF


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.