Counting curves in hyperbolic surfaces
By V. Erlandsson, Juan Souto. 2015
51 citations recorded by the source corpus.
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. For example, in the particular case that $${\Sigma}$$Σ is a once-punctured torus, we prove that the cardinality of the set of curves of type $${\gamma_0}$$γ0 and of at most length L is asymptotic to $${L^2}$$L2 times a constant.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/c02680e15530459ff537bcae1427f22b10f764c9
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In Geometry and Topology
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces (2019, background): “tion of Mirzakhani’s result and work of Erlandsson and Souto give that Theorem15.1is true even if we replace s X(L; ) with s f(L; ) = jf2MCG : f() Lgj; for any homogeneous and continuous f : C!R + [ES16]. Roughly speaking, Erlandsson and Souto show that the problem of counting s f(L; ) does not depe”