{"product_id":"9783030541538","title":"Lecture Notes in Mathematics","description":"\u003ch1\u003eLecture Notes in Mathematics\u003c\/h1\u003e \u003ch2\u003eKigami, Jun\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe 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: \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003col\u003e\n\u003cli\u003eIt is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic.\u003c\/li\u003e\n\u003cli\u003eVarious 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.\u003c\/li\u003e\n\u003cli\u003eThe Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of \u003ci\u003ep\u003c\/i\u003e-energies associated with the partition and the weight function corresponding to the metric.\u003c\/li\u003e\n\u003c\/ol\u003e\u003cp\u003e\u003c\/p\u003e These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2020-11-17\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030541538\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-54154-5\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 164\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":45369836372108,"sku":"9783030541538","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030541538.jpg?v=1775675744","url":"https:\/\/lateknightbooks.com\/products\/9783030541538","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}