Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces, Zhizhin Gennadiy Vladimirovich
Автор: Gennadiy Vladimirovich Zhizhin Название: Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces ISBN: 1799867684 ISBN-13(EAN): 9781799867685 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 26195.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Considers the construction of spaces of various dimensions from two to any finite dimension n, taking into account the indicated conditions, including zooming in on shapes, properties of geometric figures of higher dimensions, which have no analogue in three-dimensional space.
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 working in conformal geometry, analysis on metric spaces, and related areas.
Автор: Gabor Halasz; Vera T. Sos Название: Irregularities of Partitions ISBN: 3540505822 ISBN-13(EAN): 9783540505822 Издательство: Springer Рейтинг: Цена: 16070.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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