On profinite groups with finite abelianizations

Profinite groups with finite p-abelianizations arise in various contexts: group theory, number theory and geometry. Using Ph. Furtw?ngler’s transfer vanishing theorem it will be proved that a finitely generated profinite group Ĝ with this property satisfies 〚Ĝ〛) = 0 (Thm. A). As a consequence one finds that a hereditarily just-infinite non-virtually cyclic pro-p group has only one end (Cor. B). Applied to 3-dimensional Poincaré duality groups, Theorem A yields a generalization of A. Reznikov’s theorem on 3-dimensional co-compact hyperbolic lattices violating W. Thurston’s conjecture (Thm. C).     

On some configurations related to the Shelah Weak Hypothesis

We show that some cardinal arithmetic configurations related to the negation of the Shelah Weak Hypothesis and natural from the forcing point of view are impossible. Received: 8 September 1999 / Published online: 3 October 2001     

Groupwise dense families

We show that the Filter Dichotomy Principle implies that there are exactly four classes of ideals in the set of increasing functions from the natural numbers. We thus answer two open questions on consequences of ? < ?. We show that ? < ? implies that ? = ?, and that Filter Dichotomy together with ? < ? implies ? < ?. The technical means is the investigation of groupwise dense sets, ideals, filters and ultrafilters. With related techniques we prove the new inequality ?≤ cf(?). Received: 9 October 1998 / Revised version: 18 August 1999 / Published online: 21 December 2000     

Asymptotic Uniqueness of Best Rational Approximants of Given Degree to Markov Functions in L 2 of the Circle

We improve over a sufficient condition given in [8] for uniqueness of a nondegenerate critical point in best rational approximation of prescribed degree over the conjugate-symmetric Hardy space of the complement of the disk. The improved condition connects to error estimates in AAK approximation, and is necessary and sufficient when the function to be approximated is of Markov type. For Markov functions whose defining measure satisfies the Szego condition, we combine what precedes with sharp asymptotics in multipoint Padé approximation from [43], [40] in order to prove uniqueness of a critical point when the degree of the approximant goes large. This lends perspective to the uniqueness issue for more general classes of functions defined through Cauchy integrals.     

Convergence of Padé approximants for aq-hypergeometric series (Wynn's Power Series I)

We investigate the convergence of sequences of Padé approximants for power series

Regularity condition by mean oscillation to a weak solution of the 2-dimensional Harmonic heat flow into sphere

We show a regularity criterion to the harmonic heat flow from 2-dimensional Riemannian manifold M into a sphere. It is shown that a weak solution of the harmonic heat flow from 2-dimensional manifold into a sphere is regular under the criterion

Joint distributions of numbers of occurrences of a discrete pattern and weak convergence of an empirical process for the pattern

For a {0, 1}-pattern of finite length, an empirical process is introduced in order to describe the number of overlapping occurrences of the pattern at each level t[0,1] in a sequence of the corresponding indicators of i.i.d. [0, 1]-valued observations of length n. A method for obtaining the exact finite-dimensional distributions of the empirical process is given. The weak convergence of the process to a Gaussian process in D[0,1] as n tends to infinity is also established. The limiting process depends on the given pattern. The exact covariance function is compared with the asymptotic covariance function in a numerical example.     

Γ-reduction for smooth orbifolds

The aim of this short note is to show how to construct a rational Remmert reduction (the \({\widetilde \Gamma}\) -reduction) for the universal cover of smooth orbifolds (X/Δ). Doing this, we are led to introduce some singular Kähler metrics on (X/Δ) adapted to the \({\mathbb {Q}}\) -divisor Δ.