國立高雄大學圖資館 |

Language: English

Back

Geometry and analysis of metric spac...

Kigami, Jun.

Geometry and analysis of metric spaces via weighted partitions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometry and analysis of metric spaces via weighted partitionsby Jun Kigami.
Author:	Kigami, Jun.
Published:	Cham :Springer International Publishing :2020.
Description:	viii, 164 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Metric spaces.
Online resource:	https://doi.org/10.1007/978-3-030-54154-5
ISBN:	9783030541545$q(electronic bk.)

Geometry and analysis of metric spaces via weighted partitions
Kigami, Jun.

Geometry and analysis of metric spaces via weighted partitions[electronic resource] /by Jun Kigami. - Cham :Springer International Publishing :2020. - viii, 164 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v.22650075-8434 ;. - Lecture notes in mathematics ;2035..

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.

ISBN: 9783030541545$q(electronic bk.)

Standard No.: 10.1007/978-3-030-54154-5doiSubjects--Topical Terms:

186150
Metric spaces.

LC Class. No.: QA611.28 / .K54 2020

Dewey Class. No.: 514.325

Geometry and analysis of metric spaces via weighted partitions
LDR:02312nmm a2200325 a 4500 001 589667
003 DE-He213
005 20210312110019.0
006 m d
007 cr nn 008maaau
008 210601s2020 sz s 0 eng d
020 $a 9783030541545$q(electronic bk.)
020 $a 9783030541538$q(paper)
024 7 $a 10.1007/978-3-030-54154-5 $2 doi
035 $a 978-3-030-54154-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA611.28 $b .K54 2020
072 7 $a PBM $2 bicssc
072 7 $a MAT012000 $2 bisacsh
072 7 $a PBM $2 thema
082 0 4 $a 514.325 $2 23
090 $a QA611.28 $b .K47 2020
100 1 $a Kigami, Jun. $3 205657
245 1 0 $a Geometry and analysis of metric spaces via weighted partitions $h [electronic resource] / $c by Jun Kigami.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a viii, 164 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v v.2265
520 $a 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.
650 0 $a Metric spaces. $3 186150
650 1 4 $a Geometry. $3 183883
650 2 4 $a Analysis. $3 273775
650 2 4 $a Hyperbolic Geometry. $3 684054
650 2 4 $a Measure and Integration. $3 273777
650 2 4 $a Topology. $3 185965
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v 2035. $3 557764
856 4 0 $u https://doi.org/10.1007/978-3-030-54154-5
950 $a Mathematics and Statistics (SpringerNature-11649)