| 书目名称 | Geometry and Analysis of Metric Spaces via Weighted Partitions |
| 编辑 | Jun Kigami |
| 视频video | |
| 概述 | Describes how a compact metric space may be associated with an infinite graph whose boundary is the original space.Explores an approach to metrics and measures from an integrated point of view.Shows a |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | .The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text: .It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic..Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights..The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of .p.-energies associated with the partition and the weight function corresponding to the metric.. These notes should interest researchers and PhD students |
| 出版日期 | Book 2020 |
| 关键词 | Ahlfors Regular Conformal Dimension; Gromov Hyperbolicity; Infinite Graph; Metrics; Partition |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-030-54154-5 |
| isbn_softcover | 978-3-030-54153-8 |
| isbn_ebook | 978-3-030-54154-5Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 17:39:58
