论文标题
在同心球和相关集的中间维
On the intermediate dimensions of concentric spheres and related sets
论文作者
论文摘要
中级维度是Falconer，Fraser和Kempton [Arxiv：1811.06493]在2019年引入的一个尺寸系列，以在Hausdorff尺寸和盒子尺寸之间进行插值。迄今为止，关于有趣集的中间维度的明确计算的示例有限。我们计算出欧几里得空间中汇聚到原点的同心球的中间尺寸。我们还考虑了相关集，包括同心球上的孤立点和抑制拓扑医生的正弦曲线。
The intermediate dimensions are a family of dimensions introduced in 2019 by Falconer, Fraser, and Kempton [arXiv:1811.06493] to interpolate between the Hausdorff dimension and the box dimension. To date, there are limited examples of explicit calculations of the intermediate dimensions of interesting sets. We calculate the intermediate dimensions of sets of concentric spheres converging to the origin in Euclidean spaces. We also consider related sets including isolated points on concentric spheres and attenuated topologist's sine curves.
