论文标题
补充尺寸和分形几何形状
Assouad dimension and fractal geometry
论文作者
论文摘要
这是一本书，将于2020年由剑桥大学出版社出版（数学系列文章）。它着重于欧几里得空间中集合和度量的Assouad维度，以及在Assouad尺寸上的许多变体，包括较低的尺寸和Assouad Spectrum。它在分形几何形状和涵盖的主题的设置中考虑了这些概念，包括：弱切线，自相似集，自我效果集，mandelbrot渗透，kleinian群体的限制集，正交投影，距离集，距离集和Kakeya集。它还考虑了这些思想在其他领域的应用，包括：嵌入理论，数理论，概率理论和功能分析。它以开放问题的列表结尾。
This is a book to be published in 2020 by Cambridge University Press (Tracts in Mathematics Series). It focuses on the Assouad dimension of sets and measures in Euclidean space, as well as many variants on the Assouad dimension, including the lower dimension and Assouad spectrum. It considers these notions in the setting of fractal geometry and topics covered include: weak tangents, self-similar sets, self-affine sets, Mandelbrot percolation, limit sets of Kleinian groups, orthogonal projections, distance sets, and Kakeya sets. It also considers applications of these ideas to other areas, including: embedding theory, number theory, probability theory and functional analysis. It ends with a list of open problems.
