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

Author:

Gennaioli Luca,Gigli NicolaORCID

Abstract

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.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Reference19 articles.

1. Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

2. [ERS22a] Erikkson-Bique, S. , Rajala, T. , and Soultanis, E. , Tensorization of p-weak differentiable structures. Preprint, 2022. arXiv:2206.05046

3. Nonsmooth differential geometry—an approach tailored for spaces with Ricci curvature bounded from below;Gigli;Mem. Amer. Math. Soc,2018

4. Characterisation of upper gradients on the weighted Euclidean space and applications

5. Measure Theory

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3