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
SHOWING 1-10 OF 32 REFERENCES
Geometry and Spectra of Compact Riemann Surfaces
- Mathematics, Biology
- 1992
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…