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.
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.
We conjecture that for every dimension n = 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.
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)
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)
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)