## 161 Citations

Growth Rate Of Dehn Twist Lattice Points In Teichm\"{u}ller Space

- Mathematics
- 2021

Athreya, Bufetov, Eskin and Mirzakhani [2] have shown the number of mapping class group lattice points intersecting a closed ball of radius R in Teichmüller space is asymptotic to e, where h is the…

Counting curves in hyperbolic surfaces

- Mathematics
- 2015

Let $${\Sigma}$$Σ be a hyperbolic surface. We study the set of curves on $${\Sigma}$$Σ of a given type, i.e. in the mapping class group orbit of some fixed but otherwise arbitrary $${\gamma_0}$$γ0.…

Distribution in the unit tangent bundle of the geodesics of given type

- MathematicsErgodic Theory and Dynamical Systems
- 2022

Recall that two geodesics in a negatively curved surface S are of the same type if their free homotopy classes differ by a homeomorphism of the surface. In this note we study the distribution in…

Counting arcs on hyperbolic surfaces.

- Mathematics
- 2020

We give the asymptotic growth of the number of (multi-)arcs of bounded length between boundary components on complete finite-area hyperbolic surfaces with boundary. Specifically, if $S$ has genus…

ENUMERATION OF MEANDERS AND MASUR–VEECH VOLUMES

- MathematicsForum of Mathematics, Pi
- 2020

A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back…

Mirzakhani's Curve Counting

- Mathematics
- 2020

Mirzakhani wrote two papers on counting curves of given type on a surface: one for simple curves, and one for arbitrary ones. We give a complete argument deriving Mirzakhani's result for general…

SQUARE-INTEGRABILITY OF THE MIRZAKHANI FUNCTION AND STATISTICS OF SIMPLE CLOSED GEODESICS ON HYPERBOLIC SURFACES

- MathematicsForum of Mathematics, Sigma
- 2020

Given integers $g,n\geqslant 0$ satisfying $2-2g-n<0$, let ${\mathcal{M}}_{g,n}$ be the moduli space of connected, oriented, complete, finite area hyperbolic surfaces of genus $g$ with $n$ cusps. We…

A pr 2 01 8 UNIFORM BOUNDS FOR WEIL-PETERSSON CURVATURES

- Mathematics
- 2018

We find bounds for Weil-Petersson holomorphic sectional curvature, and the Weil-Petersson curvature operator in several regimes, that do not depend on the topology of the underlying surface. Among…

Uniform bounds for Weil–Petersson curvatures

- MathematicsProceedings of the London Mathematical Society
- 2018

We find bounds for Weil–Petersson holomorphic sectional curvature, and the Weil–Petersson curvature operator in several regimes, that do not depend on the topology of the underlying surface. Among…

## References

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Geometry and Spectra of Compact Riemann Surfaces

- Mathematics, Biology
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This book discusses hyperbolic structures, closed Geodesics and Huber's Theorem, and perturbations of the Laplacian in Hilbert Space.

Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces

- Mathematics
- 2006

Weil-Petersson volumes and intersection theory on the moduli space of curves

- Computer ScienceJournal of the American Mathematical Society
- 2006

A relationship between the Weil- Petersson volume and the moduli space of hyperbolic Riemann surfaces with geodesic components of lengths is established.

Proof of Theorem 3

- Mathematics
- 2005

Although f * P is a feasible solution, it is not a local optimum for θ ∈ [0, 1) and s ≤ 0 because

Simple geodesics on hyperbolic surfaces and the volume of the moduli space of curves

- Ph.D. thesis, Harvard University
- 2004

Limit points of lines of minima in Thurston's boundary of Teichmüller space

- Mathematics
- 2003

Given two measured laminations µ and ν in a hyperbolic sur-face which fill up the surface, Kerckhoff defines an associated line of minima along which convex combinations of the length functions of µ…

Series , Limit points of lines of minima in Thurston ’ s boundary of Teichmüller space , Algebr

- Geom . Topol .
- 2003

Simple Curves on Surfaces

- Mathematics, Physics
- 1999

We study simple closed geodesics on a hyperbolic surface of genus g with b geodesic boundary components and c cusps. We show that the number of such geodesics of length at most L is of order…

Hodge integrals and Gromov-Witten theory

- Mathematics
- 1998

Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these…

Simple curves on hyperbolic tori

- Mathematics
- 1995

Soit T un tore troue, muni d'une metrique hyperbolique complete, d'aire finie. Nous presentons une nouvelle approche de l'etude de l'ensemble S de toutes les geodesiques fermees simples (sans points…