Calculus of Variations and Geometric Measure Theory
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C. De Lellis - G. De Philippis - J. Hirsch

Nonclassical minimizing surfaces with smooth boundary

created by dephilipp on 22 Jun 2019
modified on 29 Jun 2019

[BibTeX]

Submitted Paper

Inserted: 22 jun 2019
Last Updated: 29 jun 2019

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.


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