A recursion for the volume of the moduli space of hyperbolic spheres

TL;DR

This paper establishes a non-linear recursive relation for calculating the volume of the moduli space of hyperbolic spheres with conical points or boundaries, extending previous results to more general cases.

Contribution

It generalizes Zograf's recursive formula from cusps to include conical points and geodesic boundaries in hyperbolic spheres.

Findings

Derived a non-linear recursive relation for moduli space volume

Extended previous recursive formulas to more general hyperbolic surfaces

Provided a new tool for computing moduli space volumes

Abstract

We prove the existence of a non-linear recursive relation for the volume of the moduli space of hyperbolic spheres with conical points or geodesic boundaries. This relation generalizes a result by Zograf, where the same was derived for cusps.