LEADER 02619oam 2200445 450 001 9910483493203321 005 20210506102323.0 010 $a3-030-54154-1 024 7 $a10.1007/978-3-030-54154-5 035 $a(CKB)4100000011586021 035 $a(DE-He213)978-3-030-54154-5 035 $a(MiAaPQ)EBC6404862 035 $a(PPN)251087115 035 $a(EXLCZ)994100000011586021 100 $a20210506d2020 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometry and analysis of metric spaces via weighted partitions /$fJun Kigami 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (VIII, 164 p. 10 illus.) 225 1 $aLecture Notes in Mathematics ;$vVolume 2265 311 $a3-030-54153-3 330 $aThe aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text: It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic. Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights. The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of p-energies associated with the partition and the weight function corresponding to the metric. These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas. 410 0$aLecture notes in mathematics ;$vVolume 2265. 606 $aConformational analysis 615 0$aConformational analysis. 676 $a541.223 700 $aKigami$b Jun$065976 801 0$bCaPaEBR 801 1$bCaPaEBR 801 2$bUtOrBLW 906 $aBOOK 912 $a9910483493203321 996 $aGeometry and Analysis of Metric Spaces via Weighted Partitions$91768616 997 $aUNINA LEADER 01637nam0 22003011i 450 001 UON00064292 005 20231205102323.123 100 $a20020107d1819 |0itac50 ba 101 $afre 102 $aFR 140 $a||||||||| ||||||||| 200 1 $aCérémonies usitées au Japon pour le mariages et les funérailles, suivies de détails sur la poudre dosia, de la préface d'un livre confutzée sur la piété filiale / le tout traduit du japonais par Feu M. Titsing 210 $aParis$cchez A. Nepveu$d1819 215 $a2 v. in 1$d8° (20 cm) 606 $aCULTURA POPOLARE$xGiappone$3UONC003567$2FI 606 $aCONFUCIANESIMO$xGiappone$3UONC004516$2FI 620 $aFR$dParis$3UONL002984 686 $aGIA XIV$cGIAPPONE - ANTROPOLOGIA, ETNOLOGIA, FOLKLORE, SPORT$2A 702 1$aTITSING$bFeu M.$3UONV041191 712 02$aA. Nepveu Libraire$3UONV078324 712 $aNepveu, A.$3UONV256397$4650 801 $aIT$bSOL$c20240220$gRICA 856 4 $uhttp://next.unior.it/sebina/repository/catalogazione/documenti/RARI GIA XIV 003 r.pdf$zRARI GIA XIV 003 r.pdf 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI$uhttp://next.unior.it/sebina/repository/catalogazione/documenti/RARI GIA XIV 003 r.pdf 912 $aUON00064292 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI RARI GIA XIV 003 $eSI MR 36196 7 003 996 $aCérémonies usitées au Japon pour le mariages et les funérailles, suivies de détails sur la poudre dosia, de la préface d'un livre confutzée sur la piété filiale$91171149 997 $aUNIOR