最小面积圆盘的存在性
Existence of least-area discs
AI总结：
本文证明欧几里得空间中每条闭Lipschitz曲线可延拓为最小面积Lipschitz圆盘，并推广至Alexandrov曲率有上界的度量空间。
AI中文摘要：
我们证明了欧几里得空间中的每条闭Lipschitz曲线都能延拓为面积最小的Lipschitz圆盘。该证明是几何性的，并且更一般地适用于Alexandrov意义下曲率有上界的度量空间。
英文摘要：
We prove that every closed Lipschitz curve in Euclidean space extends to a Lipschitz disc of least area, with Lipschitz constant controlled by that of the boundary curve. Our proof gives a new approach to the classical Douglas--Radó solution of the Plateau problem but accommodates arbitrary self-intersections and avoids Sobolev maps. The argument extends to metric spaces with curvature bounded above in the sense of Alexandrov.
