A new uniform lower bound on Weil–Petersson distance

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 sq...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2022-08, Vol.61 (4), Article 146
Main Author: Wu, Yunhui
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Fixed points (mathematics)
Geodesy
Lower bounds
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Riemann surfaces
Systems Theory
Systole
Theoretical
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Summary: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.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-022-02254-z