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.

中文翻译：

---

二维参数化整数平稳变元的规律

我们为参数化的二维平稳变元建立了最佳规律性结果。也就是说，我们表明参数化映射是一个平滑的最小分支浸入，并且多重函数是常数。我们提供了这种规律性结果的一些应用，特别是在面积泛函的变化演算中。