2019年11月27日 · I need to prove that the geodesics in a Liouville's surfaces can be obtained by primitivation of the form. My first try is to use the parallelism equations for a geodesic curve. If …

2015年7月10日 · It is referred to as the Liouville equation because its derivation for non-canonical systems utilises an identity first derived by Liouville in 1838. This suggests that the names …

Liouville’s formula. If g is a curve on the surface, and q denotes the angle of intersection of g with the curves f v =constantg, then its geodesic curvature is given by

In the mathematical field of differential geometry a Liouville surface [1] (named after Joseph Liouville) is a type of surface which in local coordinates may be written as a graph in R 3 z = f ( …

2020年10月21日 · Recent work has shown that for $γ\in (0,2)$, a Liouville quantum gravity (LQG) surface can be endowed with a canonical metric. We prove several results concerning …

2022年5月2日 · The metric associated with the Liouville quantum gravity (LQG) surface has been constructed through a series of recent works and several properties of its associated …

2022年2月11日 · Recent works have shown that there is a canonical way to to assign a metric (distance function) to a Liouville quantum gravity (LQG) surface for any parameter \ (\gamma …

We prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necess

2014年12月1日 · In this paper we will propose a definition for the geodesic distance associated to a quantum Liouville field, which can be studied numerically by putting the Liouville field on a …

2020年7月1日 · We prove that for any metric, which one can associate with a Liouville quantum gravity (LQG) surface for $\gamma \in (0,2)$ satisfying certain natural axioms, its geodesics …