Skip to main content

10 Result(s)

within Kasra Rafi Remove this filter

and

  1. Article

    Open Access

    Benjamini-Schramm convergence of periodic orbits

    We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of translation surfaces.

    Amir Mohammadi, Kasra Rafi in Geometriae Dedicata (2022)

    Download PDF (290 KB) View Article

  2. No Access

    Article

    Centralizers in Map** Class Groups and Decidability of Thurston Equivalence

    We find a constructive bound for the word length of a generating set for the centralizer of an element of the Map** Class Group. As a consequence, we show that it is algorithmically decidable whether two pos...

    Kasra Rafi, Nikita Selinger, Michael Yampolsky in Arnold Mathematical Journal (2020)

  3. No Access

    Article

    Geodesic Currents and Counting Problems

    For every positive, continuous and homogeneous function f on the space of currents on a compact surface \({{{\overline{\Sigma }}}}\) ...

    Kasra Rafi, Juan Souto in Geometric and Functional Analysis (2019)

  4. No Access

    Article

    Counting closed geodesics in strata

    We compute the asymptotic growth rate of the number \(N({{\mathcal {C}}}, R)\) ...

    Alex Eskin, Maryam Mirzakhani, Kasra Rafi in Inventiones mathematicae (2019)

  5. Article

    Maryam Mirzakhani (1977–2017)

    Pioneering mathematician and winner of the Fields Medal.

    Kasra Rafi in Nature (2017)

    Download PDF (207 KB) View Article

  6. No Access

    Article

    Bounded combinatorics and the Lipschitz metric on Teichmüller space

    Considering the Teichmüller space of a surface equipped with Thurston’s Lipschitz metric, we study geodesic segments whose endpoints have bounded combinatorics. We show that these geodesics are cobounded, and ...

    Anna Lenzhen, Kasra Rafi, **g Tao in Geometriae Dedicata (2012)

  7. No Access

    Article

    Length spectra and degeneration of flat metrics

    In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectra...

    Moon Duchin, Christopher J. Leininger, Kasra Rafi in Inventiones mathematicae (2010)

  8. No Access

    Article

    Divergence of Geodesics in Teichmüller Space and the Map** Class Group

    We show that both Teichmüller space (with the Teichmüller metric) and the map** class group (with a word metric) have geodesic divergence that is intermediate between the linear rate of flat spaces and the e...

    Moon Duchin, Kasra Rafi in Geometric and Functional Analysis (2009)

  9. No Access

    Article

    Lines of Minima and Teichmüller Geodesics

    For two measured laminations ν+ and ν− that fill up a hyperbolizable surface S and for \(t\,\in\,(-\infty,\infty)\) , ...

    Young-Eun Choi, Kasra Rafi, Caroline Series in Geometric and Functional Analysis (2008)

  10. No Access

    Article

    A Combinatorial Model for the Teichmüller Metric

    We study how the length and the twisting parameter of a curve change along a Teichmüller geodesic. We then use our results to provide a formula for the Teichmüller distance between two hyperbolic metrics on a ...

    Kasra Rafi in GAFA Geometric And Functional Analysis (2007)