Errata: On semidefinite linear complementarity problems

We correct an error in the statement of Theorem 8 in [1]. Received: January 3, 2001 / Accepted: February 26, 2001?Published online May 18, 2001     

Hypersurfaces of prescribed Gauß curvature in exterior domains

We prove an existence theorem for convex hypersurfaces of prescribed Gau? curvature in the complement of a compact set in Euclidean space which are close to a cone. Received: 23 February 2001 / Accepted: 11 May 2001 / Published online: 19 October 2001     

A Riemannian version of Korn's inequality

We prove a Korn type inequality for vector fields on a Riemann manifold. This inequality includes the special cases proved in the literature for domains in . If the domain is convex, we can considerably weaken the needed assumption on the boundary values. Received: 26 January 2001 / Accepted: 11 May 2001 / Published online: 19 October 2001     

Lieu singulier des surfaces rationnelles réglées

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

Variétés de Kummer généralisées

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

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     

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 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     

The remainder in Weyl's law for random two-dimensional

We prove that the average order of the remainder in counting the number of points of a random lattice inside a disc of radius . Our proof is spectral in nature. Submitted: July 2001, Revised: August 2001, Revised: March 2002.     

Semicontinuity of a functional depending on curvature

In this paper we prove a lower semicontinuity result for a functional , defined on a class of bounded subsets of with a piecewise boundary, with respect to the -convergence of the sets. The functional depends on the curvature of in a linear way and contains a penalizing term which prevents the appearance of thin sets in the symmetric difference , where in an -approximating sequence of . Received: 3 January 2001 / Accepted: 11 May 2001 / Published online: 19 October 2001     

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     

Estimates for derivatives of the Poisson kernels on homogeneous manifolds of negative curvature

We obtain estimates for derivatives of the Poisson kernels for the second order differential operators on homogeneous manifolds of negative curvature both in the coercive and noncoercive case. Received: 20 April 2001 / in final form: 18 August 2001 / Published online: 4 April 2002     

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     

Singhof fillings of closed 3-manifolds

We give a complete classification of all closed, connected 3-manifolds which admit a Singhof filling with any number of solid tori. Received: 15 March 2001 / Revised version: 17 September 2001     

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     

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     

On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces. Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002     

A Survey on Contractible Edges in Graphs of a Prescribed Vertex Connectivity

 The aim of the present paper is to survey old and recent results on contractible edges in graphs of a given vertex connectivity. Received: June 5, 2001 Final version received: August 23, 2001