Infinitesimal splitting for spaces with thick curve families and Euclidean embeddings
Abstract
We study metric measure spaces that admit "thick" families of rectifiable curves or curve fragments, in the form of Alberti representations or curve families of positive modulus. We show that such spaces cannot be bi-Lipschitz embedded into any Euclidean space unless they admit some "infinitesimal splitting": their tangent spaces are bi-Lipschitz equivalent to product spaces of the form Z x R k for some k 1. We also provide applications to conformal dimension and give new proofs of some previously known non-embedding results.
Main Authors
Format
Articles
Research article
Published
2024
Series
Subjects
Publication in research information system
Publisher
Institut Fourier
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202408155485Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0373-0956
DOI
https://doi.org/10.5802/aif.3606
Language
English
Published in
Annales de l'Institut Fourier
Citation
- David, G. C., & Eriksson-Bique, S. (2024). Infinitesimal splitting for spaces with thick curve families and Euclidean embeddings. Annales de l'Institut Fourier, 74(3), 973-1016. https://doi.org/10.5802/aif.3606
License
Copyright© 2024 the Authors