Approximation of length metrics by conformally flat Riemannian metrics
arXiv:2410.23304
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.
arXiv admin note: substantial text overlap with arXiv:2305.15588