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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.
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.
Describes how a compact metric space may be associated with an infinite graph whose boundary is the original space
Explores an approach to metrics and measures from an integrated point of view
Shows a relation between geometry (Ahlfors regular conformal dimension) and analysis (critical index of p-energies)
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Lecture Notes in Mathematics |
| Inhalt: |
viii
164 S. 10 s/w Illustr. 164 p. 10 illus. |
| ISBN-13: | 9783030541538 |
| ISBN-10: | 3030541533 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Kigami, Jun |
| Hersteller: |
Springer
Lecture Notes in Mathematics |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 10 mm |
| Von/Mit: | Jun Kigami |
| Erscheinungsdatum: | 17.11.2020 |
| Gewicht: | 0,271 kg |
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