Nonclassical minimizing surfaces with smooth boundary
Differential Geometry
2019-07-02 v2 Analysis of PDEs
Abstract
We construct a Riemannian metric on (arbitrarily close to the euclidean one) and a smooth simple closed curve such that the unique area minimizing surface spanned by has infinite topology. Furthermore the metric is almost K\"ahler and the area minimizing surface is calibrated.
Cite
@article{arxiv.1906.09488,
title = {Nonclassical minimizing surfaces with smooth boundary},
author = {Camillo De Lellis and Guido De Philippis and Jonas Hirsch},
journal= {arXiv preprint arXiv:1906.09488},
year = {2019}
}