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A note about charts built by Eriksson-Bique and Soultanis on metric measure spaces

Part of: Global differential geometry Classical differential geometry

Published online by Cambridge University Press:  09 June 2023

Luca Gennaioli  and
Nicola Gigli Open the ORCID record for Nicola Gigli [Opens in a new window]
Luca Gennaioli
Affiliation:
SISSA, Via Bonomea 256, Trieste, Italy e-mail: luca.gennaioli@sissa.it
Nicola Gigli*
Affiliation:
SISSA, Via Bonomea 256, Trieste, Italy e-mail: luca.gennaioli@sissa.it
*
e-mail: nicola.gigli@sissa.it
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Abstract

This note is motivated by recent studies by Eriksson-Bique and Soultanis about the construction of charts in general metric measure spaces. We analyze their construction and provide an alternative and simpler proof of the fact that these charts exist on sets of finite Hausdorff dimension. The observation made here offers also some simplification about the study of the relation between the reference measure and the charts in the setting of $\text {RCD}$ spaces.

Keywords

Chartsmetric measure spaces

MSC classification

Primary: 53A35: Non-Euclidean differential geometry 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 1 , March 2024 , pp. 49 - 59
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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