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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.

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 .

We construct an open bounded star-shaped set Ω ⊂ R 4 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.

Let X 1 , X 2 ,. .. be independent identically distributed random elements of a compact group G. We discuss the speed of convergence of the law of the product X l · · · X 1 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)

- Ursula Hamenstädt, Roman Koch
- Experimental Mathematics
- 2002

We construct an open bounded star-shaped set Ω ⊂ R 4 whose cylindrical capacity is strictly bigger than its proper displacement energy.

- 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)

- Dominique Löbach, BONNER MATHEMATISCHE SCHRIFTEN, +22 authors O. Venjakob
- 2008

In this paper we show the regularity of the strain tensor and local differentiability of the stress tensor and hardening parameters in plasticity with hardening using a viscoplastic type penalisation in the case of von Mises yield criterion. The regularity of the strain tensor was first shown by Johnson [Joh78] by constructing a bijection between the… (More)