Semi-stable models for rigid-analytic spaces

 Let R be a complete discrete valuation ring with field of fractions K and let X _K be a smooth, quasi-compact rigid-analytic space over S_p K. We show that there exists a finite separable field extension K' of K, a rigid-analytic space X' _K' over S_p K' having a strictly semi-stable formal model over the ring of integers of K', and an étale, surjective morphism f : X' _K' →X _K of rigid-analytic spaces over S_p K. This is different from the alteration result of A.J. de Jong [dJ] who does not obtain that f is étale. To achieve this property we have to work locally on X _K , i.e. our f is not proper and hence not an alteration. Received: 26 October 2001 / Revised version: 14 August 2002 Published online: 14 February 2003     

Zur Anionenselektivität von Distannylderivaten in Membranen

Anion-Selectivity of Distannyl Derivatives in Membranes A series of distannyl derivatives (2,2-bis(trimethylstannyl)-1,3-dithiane, 2,2-bis(tributylstannyl)-1,3-dithiane, hexamethyldistannane, hexabutyldistannane, hexaphenyldistannane, bis(triphenylstannyl)sulfide, o-bis(trimethylstannyl)benzene) has been studied in view of their applicability as anion-selective ionophores in solvent polymeric membranes. None of these compounds induces significant changes in the anion-selectivity pattern as compared with the membranes containing no organotin compound. Representatives with tributylstannyl groups, however, undergo chemical reactions leading to highly active anion ionophores of the type Bu₃SnX, several of which (e.g. Bu₃SnCl and Bu₃SnOH) may be present in equilibrium in the membrane phase depending on the measuring conditions.     

Trapping quasiminimizing submanifolds in spaces of negative curvature

LetM be a Hadamard manifold with all sectional curvatures bounded above by some negative constant. A well-known lemma essentially due to M. Morse states that every quasigeodesic segment inM lies within an a priori bounded distance from the geodesic arc connecting its endpoints. In this paper we establish an analogue of this fact for quasiminimizing surfaces in all dimensions and codimensions; the only additional requirement is that the sectional curvatures ofM be bounded from below as well. We apply this estimate to obtain new solutions to the asymptotic Plateau problem in various settings. The second author was supported by the Swiss National Science Foundation and enjoyed the hospitality of the University of Bonn. The collaboration between the authors was facilitated by the program GADGET II.     

Steric vs. electrostatic effects in the nucleophilic addition to a hindered cyclohexanone

The relative importance of steric vs. electrostatic effects in the nucleophilic addition to (4R,6S)-4-(tert-butyldimethylsiloxy)-2,2,6-trimethylcyclohexanone (1), a well-known chiral building block, is investigated.