论文标题
边界规则集的2D区域的密度最小化电流的密度最小
Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity
论文作者
论文摘要
在目前的工作中，我们考虑在任意编成和任意边界多样性的一般环境中最小化电流。我们研究了2D区域的边界规则性最小化电流的边界规律性，除此之外，在$（C_0，α_0，R_0）$的更一般环境中，有几个结果被指出 - 几乎将任意维度$ m $的电流最小化，并以任意多重性为边界。此外，我们不考虑边界上的任何类型的凸屏障假设，这在我们的主要规律性结果中指出，任何2D区域最小化电流$ t $的常规集（包括单方面和两侧点）是边界中的一个开放密集集。
In the present work, we consider area minimizing currents in the general setting of arbitrary codimension and arbitrary boundary multiplicity. We study the boundary regularity of 2d area minimizing currents, beyond that, several results are stated in the more general context of $(C_0, α_0, r_0)$-almost area minimizing currents of arbitrary dimension $m$ and arbitrary codimension taking the boundary with arbitrary multiplicity. Furthermore, we do not consider any type of convex barrier assumption on the boundary, in our main regularity result which states that the regular set, which includes one-sided and two-sided points, of any 2d area minimizing current $T$ is an open dense set in the boundary.
