Blar i forfatter "Erlandsson, Viveka"

Viser treff 1-5 av 5

    • Counting geodesics of given commutator length 

      Erlandsson, Viveka; Souto, Juan (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-12-15)
      Let Σ be a closed hyperbolic surface. We study, for fixed g, the asymptotics of the number of those periodic geodesics in Σ having at most length L and which can be written as the product of g commutators. The basic idea is to reduce these results to being able to count critical realizations of trivalent graphs in Σ. In the appendix, we use the same strategy to give a proof of Huber’s geometric ...

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

      Erlandsson, Viveka; Souto, Juan (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-01-24)
      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 the unit tangent bundle of the geodesics of fixed type, proving that they are asymptotically equidistributed with respect to a certain measure mS on T 1S. We study a few properties of this measure, showing ...

    • ERGODIC INVARIANT MEASURES ON THE SPACE OF GEODESIC CURRENTS 

      Erlandsson, Viveka; Mondello, Gabriele (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-10-21)
      Let be a compact, connected, oriented surface, possibly with boundary, of negative Euler characteristic. In this article we extend Lindenstrauss–Mirzakhani’s and Hamenstädt’s classification of locally finite mapping class group invariant ergodic measures on the space of measured laminations to the space of geodesic currents , and we discuss the homogeneous case. Moreover, we extend Lindenstrauss ...

    • Hyperbolic cone metrics and billiards 

      Erlandsson, Viveka; Leininger, Christopher J.; Sadanand, Chandrika (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-08-31)
      A negatively curved hyperbolic cone metric is called rigid if it is determined (up to isotopy) by the support of its Liouville current, and flexible otherwise. We provide a complete characterization of rigidity and flexibility, prove that rigidity is a generic property, and parameterize the associated deformation space for any flexible metric. As an application, we parameterize the space of ...

    • Mapping class group orbit closures for non-orientable surfaces 

      Erlandsson, Viveka; Gendulphe, Matthieu; Pasquinelli, Irene; Souto, Juan (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-05-12)
      Let S be a connected non-orientable surface with negative Euler characteristic and of finite type. We describe the possible closures in ML and PML of the mapping class group orbits of measured laminations, projective measured laminations and points in Teichmüller space. In particular we obtain a characterization of the closure in ML of the set of weighted two-sided curves.