A M\"obius Characterization of Metric Spheres

In this paper we characterize compact extended Ptolemy metric spaces with many circles up to M\"obius equivalence. This characterization yields a M\"obius characterization of the $n$-dimensional spheres $S^n$ and hemispheres $S^n_+$ when endowed with their chordal metrics. In particular, we show that every compact extended Ptolemy metric space with the property that every three points are contained in a circle is M\"obius equivalent to $(S^n,d_0)$ for some $n\ge 1$, the $n$-dimensional sphere $S^n$ with its chordal metric.Comment: 24 pages, 1 figur

Minkowski- versus Euclidean rank for products of metric spaces

We introduce a notion of the Euclidean- and the Minkowski rank for arbitrary metric spaces and we study their behaviour with respect to products. We show that the Minkowski rank is additive with respect to metric products, while additivity of the Euclidean rank only holds under additional assumptions, e.g. for Riemannian manifolds. We also study products with nonstandard product metrics.Comment: 20 pages, 1 figur

Products of hyperbolic metric spaces

Let (X_i,d_i), i=1,2, be proper geodesic hyperbolic metric spaces. We give a general construction for a ``hyperbolic product'' X_1{times}_h X_2 which is itself a proper geodesic hyperbolic metric space and examine its boundary at infinity.Comment: 17 page

Justice and the Convention on Biological Diversity

Benefit sharing as envisaged by the 1992 Convention on Biological Diversity (CBD) is a relatively new idea in international law. Within the context of non-human biological resources, it aims to guarantee the conservation of biodiversity and its sustainable use by ensuring that its custodians are adequately rewarded for its preservation. Prior to the adoption of the CBD, access to biological resources was frequently regarded as a free-for-all. Bioprospectors were able to take resources out of their natural habitat and develop commercial products without sharing benefits with states or local communities. This paper asks how CBD-style benefit-sharing fits into debates of justice. It is argued that the CBD is an example of a set of social rules designed to increase social utility. It is also argued that a common heritage of humankind principle with inbuilt benefit-sharing mechanisms would be preferable to assigning bureaucratic property rights to non-human biological resources. However, as long as the international economic order is characterized by serious distributive injustices, as reflected in the enormous poverty-related death toll in developing countries, any morally acceptable means toward redressing the balance in favor of the disadvantaged has to be welcomed. By legislating for a system of justice-in-exchange covering nonhuman biological resources in preference to a free-for-all situation, the CBD provides a small step forward in redressing the distributive justice balance. It therefore presents just legislation sensitive to the international relations context in the 21st century

Non Standard Metric Products

We consider a fairly general class of natural non standard metric products and classify those amongst them, which yield a product of certain type (for instance an inner metric space) for all possible choices of factors of this type (inner metric spaces). We further prove the additivity of the Minkowski rank for a large class of metric products.Comment: 13 pages, This paper extends the results of the second part of arXiv math.MG/0102107. Note that the first part of arXiv math.MG/0102107 has been published in Adv. Geom. 2 (2002), 123-13