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Approximation of length metrics by conformally flat Riemannian metrics

Authors :
Hip, Andres A. Contreras
Gwynne, Ewain
Publication Year :
2024

Abstract

We present a proof of the folklore result that any length metric on $\mathbb R^d$ 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.<br />Comment: arXiv admin note: substantial text overlap with arXiv:2305.15588

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2410.23304
Document Type :
Working Paper