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OverviewThe 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. Full Product DetailsAuthor: Jun KigamiPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: 1st ed. 2020 Volume: 2265 Weight: 0.454kg ISBN: 9783030541538ISBN 10: 3030541533 Pages: 164 Publication Date: 17 November 2020 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents- Introduction and a Showcase. - Partitions, Weight Functions and Their Hyperbolicity. - Relations of Weight Functions. - Characterization of Ahlfors Regular Conformal Dimension.ReviewsThe monograph is well-written and concerns a novel idea which has great potential to become a major concept in areas such as fractal geometry and dynamical systems theory. It is written at the level of graduate students and for researchers interested in the aforementioned areas. (Peter Massopust, zbMATH 1455.28001, 2021) “The monograph is well-written and concerns a novel idea which has great potential to become a major concept in areas such as fractal geometry and dynamical systems theory. It is written at the level of graduate students and for researchers interested in the aforementioned areas.” (Peter Massopust, zbMATH 1455.28001, 2021) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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