Rigidity of spherical buildings and joins

We prove a rigidity and a characterization result for buildings and spherical joins using sets of antipodal points.Received: March 2004 Revised: September 2004 Accepted: October 2004     

Sharp concentration of random polytopes

We prove that key functionals (such as the volume and the number of vertices) of a random polytope is strongly concentrated, using a martingale method. As applications, we derive new estimates for high moments and the speed of convergence of these functionals. Received: September 2004 Revision: November 2004 Accepted: November 2004     

Smash Products for Secondary Homotopy Groups

We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cup-one products, Toda brackets and Whitehead products are considered. The second author was partially supported by the Spanish Ministry of Education and Science under MEC-FEDER grants MTM2004-01865 and MTM2004-03629, the postdoctoral fellowship EX2004-0616, and a Juan de la Cierva research contract.     

Volume growth in the component of the Dehn–Seidel twist

We consider an entropy-type invariant which measures the polynomial volume growth of submanifolds under the iterates of a map, and we show that this invariant is at least 1 for every diffeomorphism in the symplectic isotopy class of the Dehn–Seidel twist. Received: April 2004 Revision: June 2004 Accepted: October 2004     

Extremality for the Vafa–Witten bound on the sphere

We prove that the round metric on the sphere has the largest first eigenvalue of the Dirac operator among all metrics that are larger than it. As a corollary, this gives an alternative proof of an extremality result for scalar curvature due to M. Llarull. Received: July 2004 Revision: October 2004 Accepted: November 2004     

On a conformal Gauss-Bonnet-Chern inequality for LCF manifolds and related topics

We establish a Gauss-Bonnet-Chern inequality for a class of complete locally conformally flat (LCF) manifolds. We also prove a finiteness theorem for a class of complete LCF four-folds with integrable Pfaffian curvature, extending the classical results of Cohn-Vossen and Huber in dimension two. This result can be viewed as a fully non-linear analogue of the Chang-Qing-Yang theorem in dimension four.Received: 13 March 2004, Accepted: 19 October 2004, Published online: 10 December 2004     

Hyperbolic groups admit proper affine isometric actions on l p -spaces

No Abstract. . Received: June2004 Revised: June2004 Accepted: June2004     

Estimates on exponential sums related to the Diffie–Hellman Distributions

No Abstract. .Received: March 2004 Revision: July 2004 Accepted: September 2004     

On rank-perfect subclasses of near-bipartite graphs

Shepherd95 proved that the stable set polytopes of near-bipartite graphs are given by constraints associated with the complete join of antiwebs only. For antiwebs, the facet set reduces to rank constraints associated with single antiwebs by Wagler2004. We extend this result to a larger graph class, the complements of fuzzy circular interval graphs, recently introduced in ChudnovskySeymour2004. Received: November 2004 / Revised version: June 2005     

On Lichtenstein’s theorem about globally conformal mappings

We present a new variational proof of the well-known fact that every Riemannian metric on a two-dimensional, simply connected domain with boundary can be represented by globally conformal parameters. From this the corresponding result for a metric on S² is derived.Received: 1 September 2004, Accepted: 13 September 2004, Published online: 10 December 2004Mathematics Subject Classification: 49Q05, 53A10, 53C42     

Regularity and relaxed problems of minimizing biharmonic maps into spheres

For and , we show that any minimizing biharmonic map from to S^k is smooth off a closed set whose Hausdorff dimension is at most n-5. When n = 5 and k = 4, for a parameter we introduce a -relaxed energy of the Hessian energy for maps in so that each minimizer of is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of for .Received: 5 April 2004, Accepted: 19 October 2004, Published online: 10 December 2004     

On the approximation of the elastica functional in radial symmetry

We prove: (1) a classification theorem for certain singularities of weak limits of immersed stable minimal hypersurfaces of arbitrary dimension and (2) a Bernstein theorem for complete immersed stable minimal hypersurfaces of dimension .Received: 1 September 2003, Accepted: 29 January 2004, Published online: 12 May 2004     

Permutations avoiding consecutive patterns, II

The generating power series for the number of permutations avoiding particular consecutive patterns are derived in a new and simple fashion.Received: 24 March 2004; revised: 28 July 2004     

The local homeomorphism property of spatial quasiregular mappings with distortion close to one

We give a quantitative proof for a theorem of Martio, Rickman and V?is?l? [MRV] on the rigidity of the local homeomorphism property of spatial quasiregular mappings with distortion close to one. The proof is based on a distortion theory established by using two main tools. First, we use a conformal invariant between sphere families and components of their preimages under quasiregular mappings. Secondly, we use Hall’s quantitative isoperimetric inequality result [H] to relate two different types of distortion. Received: April 2004 Revision: October 2004 Accepted: December 2004     

The nonlinear optimization problem in heat conduction

In this paper we study the existence and geometric properties of an optimal configuration to a nonlinear optimization problem in heat conduction. The quantity to be minimized is , where D is a fixed domain. A nonconstant temperature distribution is prescribed on and a volume constraint on the set where the temperature is positive is imposed. Among other regularity properties of an optimal configuration, we prove analyticity of the free boundary.Received: 6 October 2004, Accepted: 19 October 2004, Published online: 22 December 2004     

Energy with weight for S 2-valued maps with prescribed singularities

We generalize a result of H. Brezis, J.M. Coron and E.H. Lieb concerning the infimum of the Dirichlet energy over classes of S²-valued maps with prescribed singularities to an energy with measurable weight and we prove some geometric properties of such quantity. We also give some stability and approximation results.Received: 15 May 2004, Accepted: 19 October 2004, Published online: 22 December 2004     

Basic subgroups in abelian group rings

Suppose is a commutative ring with identity of prime characteristic and is an arbitrary abelian -group. In the present paper, a basic subgroup and a lower basic subgroup of the -component and of the factor-group of the unit group in the modular group algebra are established, in the case when is weakly perfect. Moreover, a lower basic subgroup and a basic subgroup of the normed -component and of the quotient group are given when is perfect and is arbitrary whose is -divisible. These results extend and generalize a result due to Nachev (1996) published in Houston J. Math., when the ring is perfect and is -primary. Some other applications in this direction are also obtained for the direct factor problem and for a kind of an arbitrary basic subgroup.     

Dirac-wave maps

Motivated by supersymmetric field theories, we couple the nonlinear sigma model on 1 + 1-dimensional Minkowski space with a spinor field. The corresponding Lagrangian is . The classical solutions of this model are called Dirac-wave maps. We prove that there exists a unique global solution for given Cauchy data.Received: 28 May 2004, Accepted: 9 June 2004, Published online: 16 July 2004     

Erratum to: The structure of geodetic blocks with diameter two

In our paper 1 we gave a classification of geodetic blocks of diameter two, but the proof was incorrect. Here we point out this error and give a new result about constructing geodetic blocks of diameter two. © 2004 Wiley Periodicals, Inc. J Graph Theory 46 : 79–80, 2004     

Singular limits in Liouville-type equations

We consider the boundary value problem in a bounded, smooth domain in with homogeneous Dirichlet boundary conditions. Here 0,k(x) $$ " align="middle" border="0"> is a non-negative, not identically zero function. We find conditions under which there exists a solution which blows up at exactly m points as and satisfies . In particular, we find that if , 0 $" align="middle" border="0"> and is not simply connected then such a solution exists for any given Received: 11 February 2004, Accepted: 17 August 2004, Published online: 22 December 2004