English

The regularity of parametrized integer stationary varifolds in two dimensions

Analysis of PDEs 2018-07-12 v2 Differential Geometry

Abstract

We establish an optimal regularity result for parametrized two-dimensional stationary varifolds. Namely, we show that the parametrization map is a smooth minimal branched immersion and that the multiplicity function is constant. We provide some applications of this regularity result, especially in the calculus of variations for the area functional.

Keywords

Cite

@article{arxiv.1708.02211,
  title  = {The regularity of parametrized integer stationary varifolds in two dimensions},
  author = {Alessandro Pigati and Tristan Rivière},
  journal= {arXiv preprint arXiv:1708.02211},
  year   = {2018}
}

Comments

54 pages (several typos corrected, minor improvements in the presentation, increased line spacing)