论文标题
Minkowski规范何时严格sub-convex？
When is a Minkowski norm strictly sub-convex?
论文作者
论文摘要
本文的目的是在任意拓扑的真实矢量空间上对Minkowski Norms N进行两个完整而简单的特征，以使N的Sublevel集合严格凸出。我们首先表明该属性等同于N的连续性，以及以下事实：Sublevel SET SET n^{ - 1}（[0，1））的两个点之间的任何开放弦都位于该集合内部（几何表征）。另一方面，我们证明这与说n是连续的，并且对于任意的实际数量$α$> 1，函数n^$α$严格凸（分析表征）。
The aim of this paper is to give two complete and simple characterizations of Minkowski norms N on an arbitrary topological real vector space such that the sublevel sets of N are strictly convex. We first show that this property is equivalent to the continuity of N together with the fact that any open chord between two points of the boundary of the sublevel set N^{-1}([0, 1)) lies inside that set (geometric characterization). On the other hand, we prove that this is also the same as saying that N is continuous and that for an arbitrary real number $α$ > 1 the function N^$α$ is strictly convex (analytic characterization).
