论文标题
直径与紧凑的表面和高原道格拉斯问题结合
A diameter bound for compact surfaces and the Plateau-Douglas problem
论文作者
论文摘要
在本文中，我们给出了一个几何论点，该论点是在欧几里得空间中连接的紧凑表面的直径（具有任意编成）的直径，该表面的直径为封闭表面（没有边界）的topping直径绑定。预计所获得的估计值对最小表面的最佳状态是最佳的，如果浇头猜想成立，则最佳性将遵循最佳性。我们的结果直接意味着经典高原道格拉斯问题中明确的不存在标准。我们展示了边界轮廓的示例，以确保我们的标准与基于最大原理的经典标准不同，并且基于密度估计值的标准。
In this paper we give a geometric argument for bounding the diameter of a connected compact surface (with boundary) of arbitrary codimension in Euclidean space in terms of Topping's diameter bound for closed surfaces (without boundary). The obtained estimate is expected to be optimal for minimal surfaces in the sense that optimality follows if the Topping conjecture holds true. Our result directly implies an explicit nonexistence criterion in the classical Plateau-Douglas problem. We exhibit examples of boundary contours to ensure that our criterion is of different type from classical criteria based on the maximum principle and White's criterion based on a density estimate.
