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Creators/Authors contains: "Bestvina, Mladen"

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  1. ; (, Commentarii Mathematici Helvetici)
    We study the cone of transverse measures to a fixed geodesic lamination on an infinite type hyperbolic surface. Under simple hypotheses on the metric, we give an explicit description of this cone as an inverse limit of finite-dimensional cones. We study the problem of when the cone of transverse measures admits a base and show that such a base exists for many laminations. Moreover, the base is a (typically infinite-dimensional) simplex (called aChoquet simplex) and can be described explicitly as an inverse limit of finite-dimensional simplices. We show that on any fixed infinite type hyperbolic surface, every Choquet simplex arises as a base forsomelamination. We use our inverse limit description and a new construction of geodesic laminations to give other explicit examples of cones with exotic properties. 
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  2. ; ; (, Journal of the Institute of Mathematics of Jussieu)
    Abstract We construct an unfolding path in Outer space which does not converge in the boundary, and instead it accumulates on the entire 1-simplex of projectivized length measures on a nongeometric arational$${\mathbb R}$$-treeT. We also show thatTadmits exactly two dual ergodic projective currents. This is the first nongeometric example of an arational tree that is neither uniquely ergodic nor uniquely ergometric. 
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  3. ; ; (, Annales Henri Lebesgue)
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  4. ; ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    null (Ed.)
    Abstract In this paper we prove that groups as in the title are convex cocompact in the mapping class group. 
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