On homogenization of time-dependent random flows

We study a diffusion with a random, time dependent drift. We prove the invariance principle when the spectral measure of the drift satisfies a certain integrability condition. This result generalizes the results of [13, 7]. Received: 25 February 2000 / Revised version: 11 December 2000 /?Published online: 14 June 2001     

Some variants of the logarithm

We construct certain extensions of Hodge structures using points on algebraic curves and study them. We also introduce and use a related function theory which forms a genus g > 0 version of that of classical hyperlogarithms. Received: 9 May 2000 / Revised version: 8 December 2000     

Aspects of strong compactness, measurability, and indestructibility

 We prove three theorems concerning Laver indestructibility, strong compactness, and measurability. We then state some related open questions. Received: 11 December 1999 / Revised version: 17 September 2000 / Published online: 2 September 2002 Mathematics Subject classification (2000): 03E35, 03E55 Keywords or phrases: Measurable cardinal – Strongly compact cardinal – Supercompact cardinal – Indestructibility     

The structure of Ext(A, Z) and GCH: possible co-Moore spaces

We investigate what can be when A is torsion-free and . We thereby give an answer to a question of Golasiński and Gon?alves which asks for the divisible Abelian groups which can be the type of a co-Moore space. Received: 25 January 2000; in final form: 20 June 2000 / Published online: 25 June 2001     

The minimum of quadratic functionals of the gradient on the set of convex functions

We study the infimum of functionals of the form among all convex functions such that . ( is a convex open subset of , and M is a given symmetric matrix.) We prove that this infimum is the smallest eigenvalue of M if is . Otherwise the picture is more complicated. We also study the case of an x-dependent matrix M. Received: 23 February 2000/Accepted: 4 December 2000 / Published online: 5 September 2002     

The universality of equivariant complex bordism

We show that if A is an abelian compact Lie group, all A-equivariant complex vector bundles are orientable over a complex orientable equivariant cohomology theory. In the process, we calculate the complex orientable homology and cohomology of all complex Grassmannians. Received: 14 February 2000; in final form: 4 August 2000 / Published online: 19 October 2001     

Laufer's vanishing theorem for embedded CR manifolds

Let D be a sufficiently small open subset of a generic CR manifold in . We show that the cohomology groups are either zero or infinite dimensional. Received: 2 May 2000; in final form: 6 September 2000 / Published online: 28 February 2002     

The Dirichlet problem for Weingarten hypersurfaces in Lorentz manifolds

We solve the Dirichlet problem for strictly convex, spacelike hypersurfaces of prescribed Weingarten curvature under the main assumption that there exists an upper barrier. We consider curvature functions that correspond in general to fully nonlinear elliptic partial differential equations which are not uniformly elliptic. Received: 14 April 2000; in final form: 12 September 2000 / Published online: 25 June 2001     

Inégalités de concentration pour les processus empiriques de classes de parties

We propose new concentration inequalities for maxima of set-indexed empirical processes. Our approach is based either on entropy inequalities or on martingale methods. The improvements we get concern the rate function which is exactly the large deviations rate function of a binomial law in most of the cases. Received: 11 January 2000 / Revised version: 12 May 2000 / Published online: 14 December 2000     

Large volume growth and the topology of open manifolds

In this paper, we study complete noncompact Riemannian manifolds with nonnegative Ricci curvature and large volume growth. We find some reasonable conditions to insure that this kind of manifolds are diffeomorphic to a Euclidean space or have finite topological type. Received: January 4, 2000; in final form: October 31, 2000 / Published online: 19 October 2001     

Optimal Lipschitz extensions and the infinity laplacian

We reconsider in this paper boundary value problems for “infinity Laplacian” PDE and the relationships with optimal Lipschitz extensions of the boundary data. fairly elegant new proofs, which clarify and simplify previous work, and may be characterized by a comparison principle with appropriate cones. We in comparison with cones directly implies the variational principle associated Liouville theorem for subsolutions bounded above by planes. Received: 29 May 2000 / Accepted: 12 June 2000 / Published online: 23 April 2001     

Classification of doubly-periodic minimal surfaces of genus zero

We prove that if the quotient surface of a properly embedded doubly–periodic minimal surface in ℝ³ has genus zero, then the surface is one of the classical Scherk examples. Oblatum 30-IX-1998 & 18-II-2000?Published online: 30 October 2000     

Sur le prolongement des fonctions harmoniques

We consider the extension of harmonic or subharmonic functions in the Zygmund class Λ_α with α∈]0,2[. Received: 14 April 2000 / Revised version: 1 November 2000     

On the number of partial Steiner systems

We give a simple proof of the result of Grable on the asymptotics of the number of partial Steiner systems S(t,k,m). © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 347–352, 2000     

Symmetric graph designs on friendship graphs

We settle completely the existence of symmetric graph designs on friendship graphs. © 2000 John Wiley & Sons, Inc. J Combin Designs 8:201–206, 2000     

Hall's theorem for hypergraphs

We prove a hypergraph version of Hall's theorem. The proof is topological. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 83–88, 2000     

Compact Stein surfaces with boundary as branched covers of B4

We prove that Stein surfaces with boundary coincide up to orientation preserving diffeomorphisms with simple branched coverings of B ⁴ whose branch set is a positive braided surface. As a consequence, we have that a smooth oriented 3-manifold is Stein fillable iff it has a positive open-book decomposition. Oblatum 24-II-2000 & 30-V-2000?Published online: 16 August 2000