The regularity of parametrized integer stationary varifolds in two dimensions

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.

arXiv comment54 pages (several typos corrected, minor improvements in the presentation, increased line spacing)