# Weil-Petersson volume The Weil-Petersson volume for a surface with genus $g$ and $n$ geodesic boundaries is denoted as $V_{g, n}\left(b_1, \ldots, b_n\right)$. They satisfy a recursion relation, namely [[0627 Mirzakhani recursion|Mirzakhani recursion]]. In the [[0471 String-matrix duality|JT-matrix]] duality, this recursion relation is dual to a topological recursion of the [[0197 Matrix model|matrix model]]. There is also a deformed version in [[0657 Virasoro minimal string|Virasoro minimal string]] and similarly other minimal strings. ## Refs - Fenchel-Nielsen coordinates - [[1983#Wolpert]] - intersection theory on moduli space - [[1991#Witten (Jan)]] - [[1992#Kontsevich]] - application to JT gravity - [[2019#Okuyama, Sakai]] - [[2020#Okuyama, Sakai]] - surfaces with conical defects - [[2006#Do, Norbury]] - [[2020#Turiaci, Usatyuk, Weng]] - [[2020#Witten (June, b)]] - [[2023#Eberhardt, Turiaci]] - [[2023#Artemev]]