Abstract
AbstractWe prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necessarily singular with respect to the law of any type of $$\mathrm{SLE}_\kappa $$
SLE
κ
. These hypotheses are satisfied by the LQG metric for $$\gamma =\sqrt{8/3}$$
γ
=
8
/
3
constructed by the first author and Sheffield, and subsequent work by Gwynne and the first author has shown that there is a unique metric which satisfies these hypotheses for each $$\gamma \in (0,2)$$
γ
∈
(
0
,
2
)
. As a consequence of our analysis, we also establish certain regularity properties of LQG geodesics which imply, among other things, that they are conformally removable.
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Analysis
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