Jarnik型不等式
Jarnik-type Inequalities
摘要：
这是众所周知的，由于Jarnik的一套坏的严重逼近的数字是豪斯多夫维一。如果坏（c）表示的子集x在坏的近似常数c > c（x），然后Jarnik实际上是更精确的，并给出了非平凡的下限和上界的Hausdorff维数的坏（c）的参数c > 0。我们的目的是确定一个框架上的简单条件，允许扩展“Jarnik不等式”，以进一步的例子，在应用程序中，我们讨论了一组严重逼近向量的权重和一组测地线的双曲空间，避免了一个合适的凸集的集合。
英文摘要：
It is well known due to Jarnik that the set Bad of badly approximable numbers is of Hausdorff-dimension one. If Bad(c) denotes the subset of x in Bad for which the approximation constant c > c(x), then Jarnik was in fact more precise and gave nontrivial lower and upper bounds of the Hausdorff-dimension of Bad(c) in terms of the parameter c > 0. Our aim is to determine simple conditions on a framework which allow to extend 'Jarnik's inequality' to further examples; among the applications, we discuss the set of badly approximable vectors in with weights and the set of geodesics in the hyperbolic space which avoid a suitable collection of convex sets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
