Integral formulas for compact spaceliken-submanifolds in de Sitter spaces applications to the parallel mean curvature vector case

We introduce a new method to study compact spaceliken-submanifolds in de Sitter spacesS _q ^n+q by means of certain integral formulas which have a very clear geometric meaning. As a first application of them we obtain a Bernstein type result for complete maximal submanifolds inS _q ^n+q . As for surfaces, we also get a uniqueness result for compact spacelike surfaces inS _q ^2+q with parallel mean curvature vector field. Partially supported by a DGICYT Grant No. PB91-0705-C02-02 Partially supported by a DGICYT Grant No. PB91-0731     

On the Gauss curvature of maximal surfaces in the 3-dimensional Lorentz-Minkowski space

Partially supported by DGICYT Grant PB 90-0014-C03-02.     

Orthogonal surfaces with constant mean curvature in the Euclidean 4-space

We classify orthogonal surfaces ofE ⁴ whose mean curvature is constant by proving that they are either of 1-type or of 2-type.Partially supported by a ME/Fulbright grant and by a DGICYT grant PB91-0705-C02-01     

The full automorphism groups of hyperelliptic Riemann surfaces

For every integer g≥2 we obtain the complete list of groups acting as the full automorphisms groups on hyperelliptic Riemann surfaces of genus g. Partially supported by DGICYT PB 89-201 and Science Plan 910021 Partially supported by DGICYT PB 89/379/C02/01 and Science Plan 910021 Partially supported by DGICYT After the typing of this paper we have heard about a Ph.D. Thesis by Britta Krapp on questions related to the problem studied here.     

Comparison theorems for the volume of a geodesic ball with a product of space forms as a model

We prove two comparison theorems for the volume of a geodesic ball in a Riemannian manifold taking as a model a geodesic ball in a product of two space forms.Work partially supported by the Fundació Caixa Castelló grant n. MI25043/92.Work partially supported by the DGICYT Grant No. PB91-0324.     

Stratifications distinguées comme outil en géométrie semi-analytique

We introduce the distinguish stratifications as a new tool in order to give new proofs of some essential facts in the semi-analytic geometry in an easier way, for example the property of regular separation.

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Partially supported by KBN grant PB 1219/2/91

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Partially supported by KBN grant PB 1219/2/91

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Partially supported by DGICYT.     

Weak type inequalities of maximal Hankel convolution operators

In this paper we characterize weak type (1,1) inequalities for Hankel convolution operators by means of discrete methods. Partially supported by DGICYT Grant PB 94-0591 (Spain).     

A vector valued transference of Fourier-Bessel multipliers onto Hankel multipliers with applications

In this note we prove a vector valued transference theorem relating Fourier-Bessel multipliers and Hankel multipliers. An application of such a transference theorem allows to show that results of Córdoba [3] and Romera [4] can be deduced from a recent result of Balodis and Córdoba [1, Theorem 3]. Partially supported by DGICYT Grant PB 97-1489 (Spain). Partially supported by KBN grant # 2 PO3A 034 20.     

On a theorem of Ingham

We prove a trigonometric inequality of Ingham’s type for nonharmonic Fourier series when the gap condition between frequencies does not hold any more. Partially supported by grants PB93-1203 of the DGICYT (Spain) and CHRX-CT94-04771 of the UE.     

Finite type ruled manifolds shaped on spherical submanifolds

Partially supported by a DGICYT Grant No. PS87-0115-C03.     

On nonimmersibility of compact hypersurfaces into a ball of a simply connected space form

We give a nonimmersibility theorem of a compact manifold with nonnegative scalar curvature bounded from above into a geodesic ball of a simply connected space form. Work partially supported by a DGICYT Grant No. PB91-0324 and by the E.C. Contract CHRX-CT92-0050 “G.A.D.G.E.T. II”     

Conformal geometry of surfaces in Lorentzian space forms

We study the conformal geometry of an oriented space-like surface in three-dimensional Lorentzian space forms. After introducing the conformal compactification of the Lorentzian space forms, we define the conformal Gauss map which is a conformally invariant two parameter family of oriented spheres. We use the area of the conformal Gauss map to define the Willmore functional and derive a Bernstein type theorem for parabolic Willmore surfaces. Finally, we study the stability of maximal surfaces for the Willmore functional.Dedicated to Professor T.J. WillmoreSupported by an FPPI Postdoctoral Grant from DGICYT Ministerio de Educación y Ciencia, Spain 1994 and by a DGICYT Grant No. PB94-0750-C02-02     

On lower bounds for theL 2-Wasserstein metric in a Hilbert space

We provide two families of lower bounds for theL ²-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02.     

Dido's problem in the plane for domains with fixed diameter

We find the connected compact domains in the closed half-plane, with fixed area and diameter, which minimize the relative perimeter.This work has been partially supported by the DGICYT (Spain) Grant no. PB 91-0324.     

Density conditions for interpolation inA −∞

We give a necessary and sufficient density condition for a sequence {a _k} _k in the unit disk ofC to be interpolating for the classA ^−∞ of holomorphic functions with polynomial growth. The condition goes along the lines of those found by Seip for the analogous problem in Bergman spaces of the disk and by Berenstein and Li for some weighted spaces of entire functions. The result complements an earlier characterization given by Bruna and Pascuas. Partially supported by DGICYT grant PB95-0956-C02-02 and CIRIT grant 1998 SGR 00052. Also supported by a program of the Comunitat de Treball dels Pirineus.     

Pick invariant and affine Gauss-Kronecker curvature

The elliptic paraboloid and the homogeneous affine surface given by (u, v, 1/2(u ²+v ^–2/3)),v>0, are characterized as locally strongly convex affine surfaces inA, with constant Pick invariant and vanishing affine Gauss-Kronecker curvature.Research partially supported by DGICYT Grant PB90-0014-C03-02.     

The moduli spaces of rank 2 stable vector bundles over Veronesean surfaces

Partially supported by DGICYT PB88-0224     

On the number of generators of modules over Laurent rings

Partially supported by DGICYT PB88-0224     

On the number of generators of modules over polynomial affine rings

Partially supported by DGICYT PB88-0224     

An algorithm to compute orders and ramification indices of cyclic actions on compact surfaces,II

In this paper we obtain an effective algorithm to compute all even orders and ramification indices of homeomorphisms of finite order acting on compact surfaces, orientable or not. This completes the case of odd orders, previously studied by the authors. E. Bujalance and A. F. Costa were partially supported by DGICYT PB 92-0716 and CEE-CHRX-CT93-0408. J. M. Gamboa was partially supported by DGICYT PB 92-0498-C02-02 and CEE-CHRX-CT93-0408. J. Lafuente was partially supported by DGICYT PB 92-0220.