Let X be a Banach space and let C closed convex bounded subset of . It is proved that weakly compact if, only has the generic fixed point property ( G -FPP) for class L -bi-Lipschitz affine mappings every > 1 also if Pełczyński's u ), then either compact, contains an ℓ -sequence or c 0 -summing basic sequence. In this case, weak compactness equivalent to -FPP strengthened are uniformly bi-Lipsc...

Abstract Every integral current in a locally compact metric space X can be approximated by Lipschitz chain with respect to the normal mass, provided that maps into extended slightly.

We prove a local limit theorem for Lipschitz continuous observables on a weakly coupled lattice of piecewise expanding interval maps. The core of the paper is a proof that the spectral radii of the Fourier-transfer operators for such a system are strictly less than 1. This extends the approach of [KL06] where the ordinary transfer operator was studied.

The goal of these notes is to introduce the reader to the Heisenberg group with its CarnotCarathéodory metric and to Pansu’s differentiation theorem. As they are very similar, we will first study Rademacher’s theorem about Lipschitz maps and then see how the same technique can be applied in the more complex setting of the Heisenberg group.

We generalize Kirszbraun’s extension theorem for Lipschitz maps between (subsets of) euclidean spaces to metric spaces with upper or lower curvature bounds in the sense of A.D. Alexandrov. As a byproduct we develop new tools in the theory of tangent cones of these spaces and obtain new characterization results which may be of independent interest.