Lieu singulier des surfaces rationnelles réglées

Sans résumé Received: 9 October 2001; in final form: 10 December 2001 / Published online: 29 April 2002     

Benchmarking optimization software with performance profiles

We propose performance profiles — distribution functions for a performance metric — as a tool for benchmarking and comparing optimization software. We show that performance profiles combine the best features of other tools for performance evaluation. Received: February 2001 / Accepted: May 2001?Published online October 2, 2001     

A partial regularity result for harmonic maps into a Finsler manifold

In this paper, we consider the energy of maps from an Euclidean space into a Finsler space and study the partial regularity of energy minimizing maps. We show that the -dimensional Hausdorff measure of the singular set of every energy minimizing map is 0 for some , when m=3,4. Received: 6 June 2001 / Accepted: 10 July 2001 / Published online: 12 October 2001     

A Bernstein theorem for special Lagrangian graphs

We obtain a Bernstein theorem for special Lagrangian graphs in for arbitrary n only assuming bounded slope but no quantitative restriction. Received: 18 January 2001 / Accepted: 7 June 2001 / Published online: 12 October 2001 The second-named author is grateful to the Max Planck Institute for Mathematics in the Sciences in Leipzig for its hospitality and support and also 973 project in China.     

Variétés de Kummer généralisées

Re?u le 22 mars 2001; forme finale: 18 juin 2001 / Published online: 1 February 2002     

The Dirichlet problem at infinity for harmonic map equations arising from constant mean curvature surfaces in the hyperbolic 3-space

The purpose of this paper is to study some uniqueness, existence and regularity properties of the Dirichlet problem at infinity for proper harmonic maps from the hyperbolic m-space to the open unit n-ball with a specific incomplete metric. When m=n=2, harmonic solutions of this Dirichlet problem yield complete constant mean curvature surfaces in the hyperbolic 3-space. Received: 25 January 2001 / Accepted: 23 February 2001 / Published online: 25 June 2001     

Algebraic models for equivariant homotopy theory over Abelian compact Lie groups

We describe some algebraic models for equivariant rational and p-adic homotopy theory over Abelian compact Lie groups. Received: 12 February 2001; in final form: 15 August 2001 / Published online: 28 February 2002     

History of mathematical programming in the USSR: analyzing the phenomenon

I am not a historian; these are just reminiscences of a person involved in the development of optimization theory and methods in the former USSR. I realize that my point of view may be very personal; however, I am trying to present as broad and unbiased picture as I can. Received: January 29, 2001 / Accepted: May 17, 2001?Published online October 2, 2001     

On Euler–Jaczewski sequence and Remmert–Van de Ven problem for toric varieties

Let X be a complete toric variety and Y a smooth projective variety with . We prove that, if is a surjective morphism then . Received: 15 May 2001; in final form: 22 October 2001/ Published online: 4 April 2002     

Equicontinuity of families of plurisubharmonic functions with bounds on their Monge-Ampère masses

It is proved that families of solutions of the complex Monge-Ampère equation with fixed boundary values and certain bounds on the right hand side are equicontinuous. Received: 24 April 2001; in final form: 10 August 2001 / Published online: 28 February 2002     

Hessian equations on compact non-negatively curved riemannian manifolds

On a compact connected riemannian manifold, we partly extend to hessian equations an existence result proved for Monge-Ampère equations. Non-negative curvature is required for a priori estimates. Received: 13 July 2001 / Accepted: 25 October 2001 / Published online: 29 April 2002 The author is supported by the CNRS     

The doubly periodic Costa surfaces

We derive global Weierstrass representations for complete minimal surfaces obtained by substituting the planar end of the Costa surface by symmetry curves. Received: 14 February 2001; in final form: 24 April 2001 / Published online: 29 April 2002     

Combinatorial structure of some hyperbolic buildings

We give an elementary construction of polyhedra whose links are connected bipartite graphs. In particular, we construct polyhedra whose links are generalized m-gons. The polyhedra of this type are interesting because of their universal coverings, which are two-dimensional hyperbolic buildings. Received: 10 March 2001; final form: 26 November 2001/ Published online: 29 April 2002     

Enclosure theorems for extremals of elliptic parametric functionals

In the following paper we study parametric functionals. First we introduce a generalized mean curvature (so called F-mean curvature). This enables us to describe extremals of parametric funcionals as surfaces of prescribed F-mean curvature. Furthermore we give a differential equation for arbitrary immersions generalizing and apply this equation to surfaces of vanishing and prescribed F-mean curvature. Especially we prove non-existence results for such surfaces generalizing Theorems by Hildebrandt and Dierkes [3], [6]. Received: 11 May 2001 / Accepted: 11 July 2001 / Published online: 12 October 2001     

A unimodularly invariant theory for immersions into the affine space

We develop a unimodularly invariant theory for immersions with higher codimension into the affine space. Received: 6 September 2001; in final form: 22 November 2001 / Published online: 29 April 2002 RID="*" ID="*" Supported by the Deutsche Forschungsgemeinschaft     

Linear embeddings of semialgebraic G-spaces

Let G be a compact semialgebraic linear group. We prove that every regular semialgebraic G-space admits a semialgebraic G-embedding into some semialgebraic orthogonal representation space of G. Received: 9 January 2001; in final form: 17 August 2001 / Published online: 28 February 2002     

Seifert unions of solid tori

We obtain a list of all 3-manifolds that can be obtained by gluing 3-balls and solid tori along mutually disjoint surfaces in their boundaries. Received: 22 February 2001; in final form: 18 October 2001 / Published online: 4 April 2002     

On Hausdorff dimension of invariant measures arising from non-contractive iterated function systems

Under rather general assumptions we give an upper and lower bound estimate of the Hausdorff dimension of the invariant probability measure for an iterated function systems acting on a Polish space. Received: May 2, 2001; in final form: July 30, 2001?Published online: May 29, 2002     

On symplectic cobordisms

In this note we make several observations concerning symplectic cobordisms. Among other things we show that every contact 3-manifold has infinitely many concave symplectic fillings and that all overtwisted contact 3-manifolds are “symplectic cobordism equivalent”. Received: 26 March 2001 / Revised version: 1 May 2001 / Published online: 28 February 2002     

Feynman’s Operational Calculi: Disentangling Away from the Origin

In this paper we develop a method of forming functions of noncommuting operators (or disentangling) using functions that are not necessarily analytic at the origin in ℂ ⁿ . The method of disentangling follows Feynman’s heuristic rules from in (Feynman in Phys. Rev. 84:18–128, 1951) a mathematically rigorous fashion, generalizing the work of Jefferies and Johnson and the present author in (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001). In fact, the work in (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001) allow only functions analytic in a polydisk centered at the origin in ℂ ⁿ while the method introduced in this paper enable functions that are not analytic at the origin to be used. It is shown that the disentangling formalism introduced here reduces to that of (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001) under the appropriate assumptions. A basic commutativity theorem is also established.