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Geometry and Analysis of Metric Spaces via Weighted Partitions
Engelsk
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Specifikationer
Sprog:
Engelsk
Sider:
164
ISBN-13:
9783030541538
Indbinding:
Paperback
Udgave:
ISBN-10:
3030541533
Udg. Dato:
17 nov 2020
Længde:
0mm
Bredde:
155mm
Højde:
235mm
Forlag:
Springer Nature Switzerland AG
Serie:
Lecture Notes in Mathematics
Oplagsdato:
17 nov 2020
Forfatter(e):
Paperback
Format:

Om denne bog
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.

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Specifikationer
Sprog:
Engelsk
Sider:
164
ISBN-13:
9783030541538
Indbinding:
Paperback
Udgave:
ISBN-10:
3030541533
Udg. Dato:
17 nov 2020
Længde:
0mm
Bredde:
155mm
Højde:
235mm
Forlag:
Springer Nature Switzerland AG
Serie:
Lecture Notes in Mathematics
Oplagsdato:
17 nov 2020
Forfatter(e):
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