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Providing each simplex in C(S) with the standard euclidean metric of side-length 1 equips the complex of curves with the structure of a geodesic metric space whose isometry group is just M̃g,m (except for the twice punctured torus). However, this metric space is not locally compact. Masur and Minsky [MM1] showed that nevertheless the geometry of C(S) can be… (More)

For g ≥ 0 and m ≥ 1 such that 2g−2+m ≥ 1 let Tg,m be the Teichmüller space of hyperbolic metrics on a surface of genus g with m punctures, and let ∂Tg,m be its Thurston boundary. Using geodesic length functions, we construct a homeomorphism of Tg,m ∪ ∂Tg,m onto a convex finite-sided polyhedron in RP 6g−6+2m .

Using train tracks on a non-exceptional oriented surface S of finite type in a systematic way we give a proof that the complex of curves C(S) of S is a hyperbolic geodesic metric space. We also discuss the relation between the geometry of the complex of curves and the geometry of Teichmüller space.

In the paper [B-C-G] Besson, Courtois and Gallot proved the following remarkable theorem: Let S be a closed rank 1 locally symmetric space of noncompact type and let M be a closed manifold of negative curvature which is homotopy equivalent to S. If S and M have the same volume and the same volume entropies (i.e. the same asymptotic growth rate of volumes of… (More)

We construct an open bounded star-shaped set Ω ⊂ R whose cylindrical capacity is strictly bigger than its proper displacement energy. We also construct an open bounded set Ω0 ⊂ R 4 whose proper displacement energy is stricly bigger than the displacement energy of its closure. 1

Let T (S) be the Teichmüller space of an oriented surface S of finite type. We discuss the action of subgroups of the mapping class group of S on the CAT(0)-boundary of the completion of T (S) with respect to the Weil-Petersson metric. We show that the set of invariant Borel probability measures for the Weil-Petersson flow on moduli space which are… (More)

Let X1, X2, . . . be independent identically distributed random elements of a compact group G. We discuss the speed of convergence of the law of the product Xl · · ·X1 to the Haar measure. We give poly-log estimates for certain finite groups and for compact semi-simple Lie groups. We improve earlier results of Solovay, Kitaev, Gamburd, Shahshahani and… (More)

- Ulrich Schlickewei, BONNER MATHEMATISCHE SCHRIFTEN, +14 authors M. Schäl
- 2009

Angefertigt mit der Genehmigung der Mathematisch-Summary This thesis consists of four parts all of which deal with different aspects of Hodge classes on self-products of K3 surfaces. In the first three parts we present three different strategies to tackle the Hodge conjecture for self-products of K3 surfaces. The first approach is of deformation theoretic… (More)

We conjecture that for every dimension n 6=3 there exists a noncompact hyperbolic n-manifold whose volume is smaller than the volume of any compact hyperbolic n-manifold. For dimensions n≤ 4 and n = 6 this conjecture follows from the known results. In this paper we show that the conjecture is true for arithmetic hyperbolic n-manifolds of dimension n≥ 30.… (More)

Let S be a closed oriented surface S of genus g ≥ 0 with m ≥ 0 marked points (punctures) and 3g − 3 + m ≥ 2. This is a survey of recent results on actions of the mapping class group of S which led to a geometric understanding of this group. Mathematics Subject Classification (2010). Primary 30F60, Secondary 20F28, 20F65, 20F69