Uniqueness of the welding problem for SLE and Liouville quantum gravity

Oliver McEnteggart, Jason Miller, Wei Qian

We give a simple set of geometric conditions on curves $\eta$, $\tilde{\eta }$ in $\mathbf{H}$ from $0$ to $\infty$ so that if $\phi :\mathbf{H}\to \mathbf{H}$ is a homeomorphism whic…