The coordinate change formula for the Liouville quantum gravity metric holds for all conformal maps simultaneously

Charles Devlin VI

Liouville quantum gravity (LQG) is, heuristically, a theory of random Riemannian geometry with Riemannian metric tensor $e^{\gamma h}(\mathrm{d}{x}^2+\mathrm{d}{y}^2)$, where $h$ is a v…