Convex geodesic bicombings and hyperbolicity

A geodesic bicombing on a metric space selects for every pair of points a geodesic connecting them. We prove existence and uniqueness results for geodesic bicombings satisfying different convexity conditions. In combination with recent work by the second author on injective hulls, this shows that every word hyperbolic group acts geometrically on a proper, finite dimensional space X with a unique (hence equivariant) convex geodesic bicombing of the strongest type. Furthermore, the Gromov boundary of X is a Z-set in the closure of X, and the latter is a metrizable absolute retract, in analogy with the Bestvina--Mess theorem on the Rips complex.Comment: 22 page

Flats in spaces with convex geodesic bicombings

In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales. We show that some such results remain valid for metric spaces with non-unique geodesic segments under suitable convexity assumptions on the distance function along distinguished geodesics. The discussion includes, among other things, the Flat Torus Theorem and Gromov's hyperbolicity criterion referring to embedded planes. This generalizes results of Bowditch for Busemann spaces.Comment: Final version, to appear in Analysis and Geometry in Metric Spaces (AGMS

Lipschitz extensions of maps between Heisenberg groups

Let \H^n be the Heisenberg group of topological dimension $2n+1$. We prove that if $n$ is odd, the pair of metric spaces (\H^n, \H^n) does not have the Lipschitz extension property

Local Currents in Metric Spaces

Ambrosio and Kirchheim presented a theory of currents with finite mass in complete metric spaces. We develop a variant of the theory that does not rely on a finite mass condition, closely paralleling the classical Federer-Fleming theory. If the underlying metric space is an open subset of a Euclidean space, we obtain a natural chain monomorphism from general metric currents to general classical currents whose image contains the locally flat chains and which restricts to an isomorphism for locally normal currents. We give a detailed exposition of the slicing theory for locally normal currents with respect to locally Lipschitz maps, including the rectifiable slices theorem, and of the compactness theorem for locally integral currents in locally compact metric spaces, assuming only standard results from analysis and measure theor

Impact of VAT Exemptions in the Postal Sector on Competition and Welfare

The focus of our paper is on the competitive effects of the proposed VAT regime relative to selected alternatives. We also highlight the welfare effects of various VAT scenarios. While an exempt operator cannot reclaim VAT paid on inputs (relevant for non-labor inputs only) and therefore faces higher costs ceteris paribus, an important fraction of customers of non-exempt operators will not be able to deduct VAT themselves. Hence, the exempt incumbent operator has on the one hand a cost disadvantage, and on the other, a price advantage. The net effect will depend on the fraction of non-labor inputs relative to the fraction of non-rated customers. We report market shares, optimum prices, tax revenue and welfare in a liberalized postal market. The various scenarios differ by the operators’ VAT status. We also take into account the fraction of non-rated customers that cannot deduct VAT themselves. The paper sheds light on the main competitive impact of VAT policies while showing the consequences on overall welfare. We show that the results are very sensitive to the operators’ labor policies. Consequently, VAT exemptions have a different impact in countries with different labor regulations. The comprehensive treatment of competition and welfare enables us to provide guidance on how to resolve the policy trade-off between consumer surplus, government tax revenue, and a level playing field in liberalized postal markets.Value Added Taxation, Regulation, Post, Competition, Welfare

Metric stability of trees and tight spans

We prove optimal extension results for roughly isometric relations between metric ( $${\mathbb{R}}$$ R -)trees and injective metric spaces. This yields sharp stability estimates, in terms of the Gromov-Hausdorff (GH) distance, for certain metric spanning constructions: the GH distance of two metric trees spanned by some subsets is smaller than or equal to the GH distance of these sets. The GH distance of the injective hulls, or tight spans, of two metric spaces is at most twice the GH distance between themselve

Affinity Constants of Naturally Acquired and Vaccine-Induced Anti-Pseudomonas aeruginosa Antibodies in Healthy Adults and Cystic Fibrosis Patients

Naturally acquired anti-Pseudomonas aeruginosa antibody fails to afford protection against repeated P. aeruginosa bronchopulmonary exacerbations in cystic fibrosis (CF) patients. In an effort to explain this phenomenon, the titer and affinity constants of serum anti-lipopolysaccharide (LPS) IgG were determined in five study groups: healthy adults before and after immunization with a polyvalent LPS-based vaccine, healthy noncolonized CF patients before and after immunization, nonimmunized CF patients with significantly elevated anti-LPS antibody titers without documented colonization, recently colonized CF patients before and after immunization, and nonimmunized CF patients chronically colonized with P. aeruginosa. Immunization elicited a significant rise in total anti-LPS immunoglobulin levels and affinity constants in both healthy adults and CF patients. Although chronically colonized patients had elevated levels of total anti-LPS antibody, these antibodies possessed affinities at least tOO-fold less than those of vaccine-induced antibodie