论文标题
在Busemann-Hausdorff二维和二拟合二的密度，并应用了高原问题
On Busemann--Hausdorff densities of dimension two and of codimension two, with an application to Plateau Problem
论文作者
论文摘要
本文的目的是双重的。首先，我们描述了一个（大概是）新案例，其中Busemann-Hausdorff密度是凸。我们应用相应的结果来证明在复杂的有限尺寸规范矢量空间中，将编成二拟构感的链的可整流链最小化。其次，我们证明，对于每个$ n \ geq 4 $，存在一个$ n $尺寸的规范空间，其中相应的二维Busemann-Hausdroff密度并不完全凸出。这给出了H. Busemann和E. Strauss提出的问题的负面答案。
The purpose of this paper is twofold. First, we describe one (presumably) new case, in which Busemann--Hausdorff densities are convex. We apply the corresponding result to prove the existence of minimizing rectifiable chains of codimension two in complex finite dimensional normed vector spaces. Second, we prove that for each $n\geq 4$, there exists an $n$ dimensional normed space in which the corresponding two dimensional Busemann--Hausdroff density is not totally convex. This gives a negative answer to a question posed by H. Busemann and E. Strauss.
