An integral inequality for compact maximal surfaces inn-dimensional de Sitter space and its applications

In this paper we prove an integral inequality for the Gaussian curvature of compact maximal surfaces inn-dimensional de Sitter space. Some applications of that inequality are given in order to solve the associated Bernstein type problem as well as to characterize the totally geodesic immersion in terms of its area and the first nontrivial eigenvalue of its Laplacian.Partially supported by a DGICYT Grant No. PB91-0705-C02-02Partially supported by a DGICYT Grant No. PB91-0731     

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     

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.     

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

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

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.     

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.     

Pointwise multipliers and decomposition theorems in <Emphasis Type="Italic">F</Emphasis><Superscript><Emphasis Type="Italic">∞,q</Emphasis></Superscript><Subscript><Emphasis Type="Italic">s</Emphasis></Subscript>

In this paper we give a characterization of the pointwise multipliers of the holomorphic Triebel-Lizorkin spaces F^{, q}_s, and we apply these results to prove a corona decomposition theorem for these spaces.Mathematics Subject Classification (1991):32A37Both authors partially supported by DGICYT Grant BMF2002-04072-C02-01 and CIRIT Grant 2001-SGR-00172     

Weighted bounds for the carleson maximal operator inR n

The Carleson maximal operator is shown to be bounded inL ^p (w) for certain values ofp and certain radial weightsw when acting on products of radial functions and homogeneous harmonic polynomials. Partially supported by DGICYT (MEC Spain). PB 92/187.     

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     

Submanifolds in pseudo-Euclidean spaces satisfying the condition Δx=Ax+B

In this paper we study pseudo-Riemannian submanifolds in ℝ _n ^+k/t satisfying the condition Δx=Ax+B, whereA is an endomorphism of ℝ _n ^+k/t andB is a constant vector in ℝ _n ^+k/t . We give a characterization theorem whenA is a self-adjoint endomorphism. As for hypersurfaces we are able to obtain a classification theorem for any endomorphismA. Supported by a FPI Grant, DGICYT, 1990. Partially supported by a DGICYT Grant No. PS87-0115-C03-03.     

On the topological type of anticonformal square roots of automorphisms of Riemann surfaces

Let X be a compact Riemann surface and f be a conformal automorphism of X of order n. An anticonformal square root of f is an anticonformal automorphism g of X such that g²=f. If g₁ and g₂ are two anticonformal square roots of f we study the problem of whether g₁ and g₂ have the same topological type, i. e., if there exists a homeomorphism h:X→X such that g₁=hg₂h⁻¹. We use techniques of noneuclidean crystallographic (NEC) groups and the topological classification of orientation reversing maps of finite period on surfaces given in [C1] and [Y]. Partially supported by DGICYT PB92-0716 and EC project CHRX-CT93-408     

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.     

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”     

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.     

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.     

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.     

Surfaces with Vanishing Moebius Form in <Emphasis Type="Italic">S</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

An important Moebius invariant in the theory of Moebius surfaces in S^n is the so-called Moebius form. In this paper,we give a complete classification of surfaces in S^n with vanishing Moebius form under the Moebius transformation group.     

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

In this paper we get an effective algorithm to compute all odd orders and ramification indices of homeomorphisms acting on compact surfaces, orientable or not. E. Bujalance and A. F. Costa were partially supported by DGICYT PB 89-201 and Science Plan N SC1-CT91-0716, J. M. Gamboa was partially supported by DGICYT PB 89-379 and Science Plan N SC1-CT91-0716, and J. Lafuente was partially supported by Science Plan N SC1-CT91-0716.     

Embedded minimal surfaces: Forces,topology and symmetries

We prove topological uniqueness theorems for embedded minimal surfaces in ³ under the assumption that certain forces associated to these surfaces are vertical. We give applications to minimal surfaces with symmetries and with free boundary.Partially supported by DGICYT grant PB94-0796     

On maximal surfaces in the n-dimensional Lorentz-Minkowski space

Complete maximal surfaces in the n-dimensional Lorentz-Minkowski space are studied from the behaviour of their normal vectors. Moreover, several examples of maximal surfaces are constructed.Research partially supported by DGICYT Grant PS87-0115-C03-02.