A new uniform lower bound on Weil-Petersson distance

Abstract

In this paper we study the injectivity radius based at a fixed point along Weil-Petersson geodesics. We show that the square root of the injectivity radius based at a fixed point is $0.3884$-Lipschitz on Teichmüller space endowed with the Weil-Petersson metric. As an application we reprove that the square root of the systole function is uniformly Lipschitz on Teichmüller space endowed with the Weil-Petersson metric, where the Lipschitz constant can be chosen to be $0.5492$. Applications to asymptotic geometry of moduli space of Riemann surfaces for large genus will also be discussed.

Calculus of Variations and Partial Differential Equations, to appear. 30 pages, 1 figure

References in corpus (3)

• Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
• Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures
• Systole functions and Weil-Petersson geometry

Cited by in corpus (2)

• Systole functions and Weil-Petersson geometry
• Shape of filling-systole subspace in surface moduli space and critical points of systole function