Approximation of length metrics by conformally flat Riemannian metrics
Differential Geometry
2024-11-01 v1 Metric Geometry
Probability
Abstract
We present a proof of the folklore result that any length metric on can be approximated by conformally flat Riemannian distance functions in the uniform distance. This result is used to study Liouville quantum gravity in another paper by the same authors.
Cite
@article{arxiv.2410.23304,
title = {Approximation of length metrics by conformally flat Riemannian metrics},
author = {Andres A. Contreras Hip and Ewain Gwynne},
journal= {arXiv preprint arXiv:2410.23304},
year = {2024}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2305.15588