English

Nonclassical minimizing surfaces with smooth boundary

Differential Geometry 2019-07-02 v2 Analysis of PDEs

Abstract

We construct a Riemannian metric gg on R4\mathbb{R}^4 (arbitrarily close to the euclidean one) and a smooth simple closed curve ΓR4\Gamma\subset \mathbb R^4 such that the unique area minimizing surface spanned by Γ\Gamma has infinite topology. Furthermore the metric is almost K\"ahler and the area minimizing surface is calibrated.

Keywords

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}
}
R2 v1 2026-06-23T10:00:47.871Z