An eigenvalue problem for the biharmonic operator on Z(2)-symmetric regions

In this work we show that the eigenvalues of the Dirichlet problem for the biharmonic operator are generically simple in the set Of Z(2)-symmetric regions of R-n, n >= 2, with a suitable topology. To accomplish this, we combine Baire`s lemma, a generalised version of the transversality theorem, due to Henry [Perturbation of the boundary in boundary value problems of PDEs, London Mathematical Society Lecture Note Series 318 (Cambridge University Press, 2005)], and the method of rapidly oscillating functions developed in [A. L. Pereira and M. C. Pereira, Mat. Contemp. 27 (2004) 225-241].

Bjorling problem for timelike surfaces in the Lorentz-Minkowski space

We solve the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space through a split-complex representation formula obtained for this kind of surface. Our approach uses the split-complex numbers and natural split-holomorphic extensions. As applications, we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate Bjorling problems in the Lorentz-Minkowski space. (C) 2010 Elsevier Inc. All rights reserved.

Decomposability problem on branched coverings

Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected closed surface N with chi(N) <= 0. This shows that decomposable and indecomposable realizations may coexist. Moreover, we characterize the branch data of a decomposable primitive branched covering. Bibliography: 20 titles.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

New classes of spatial central configurations for the n+3-body problem

In this paper, we show the existence of new families of spatial central configurations for the n + 3-body problem, n >= 3. We study spatial central configurations where n bodies are at the vertices of a regular n-gon T and the other three bodies are symmetrically located on the straight line that is perpendicular to the plane that contains T and passes through the center of T. The results have simple and analytic proofs. (c) 2010 Elsevier Ltd. All rights reserved.

Stacked central configurations for the spatial six-body problem

In this paper we show the existence of three new families of stacked spatial central configurations for the six-body problem with the following properties: four bodies are at the vertices of a regular tetrahedron and the other two bodies are on a line connecting one vertex of the tetrahedron with the center of the opposite face. (c) 2009 Elsevier B.V. All rights reserved.