Authors:M. Dajczer; J. H. de Lira Pages: 187 - 198 Abstract: In this paper, we provided conditions for an entire constant mean curvature Killing graph lying inside a possible unbounded region to be necessarily a slice. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0019-3 Issue No:Vol. 48, No. 2 (2017)

Authors:Wolfgang Ebeling; Sabir M. Gusein-Zade Pages: 199 - 208 Abstract: For a complex analytic variety with an action of a finite group and for an invariant 1-form on it, we give an equivariant version (with values in the Burnside ring of the group) of the local Euler obstruction of the 1-form and describe its relation with the equivariant radial index defined earlier. This leads to equivariant versions of the local Euler obstruction of a complex analytic space and of the global Euler obstruction. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0022-8 Issue No:Vol. 48, No. 2 (2017)

Authors:Jiryo Komeda; Akira Ohbuch Pages: 209 - 218 Abstract: Let (C, P) be a pointed non-singular curve of genus g such that the Weierstrass semigroup H(P) of P is \(\gamma \) -hyperelliptic. We prove that there exists a double covering \(\pi :C\longrightarrow C'\) such that P is its ramification point if \(g=6\gamma +1\) , \(6\gamma \) and \(H(P)\not \ni 4\) . Torres showed that the above statement holds if \(g\ge 6\gamma +4\) . Kato and the authors also obtained the same result even in the cases \(g=6\gamma +3\) and \(6\gamma +2\) . PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0002-z Issue No:Vol. 48, No. 2 (2017)

Authors:F. E. Brochero Martínez; M. Corrêa; A. M. Rodríguez Pages: 219 - 235 Abstract: We give an upper bound of the degree of quasi-smooth hypersurfaces which are invariant by a one dimensional holomorphic foliation on a weighted projective space. This bound depends only on the degree of the foliation and the weights of the space. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0003-y Issue No:Vol. 48, No. 2 (2017)

Authors:Edileno de Almeida Santos Pages: 237 - 251 Abstract: We consider singular holomorphic foliations on compact complex surfaces with invariant rational nodal curve of positive self-intersection. Then, under some assumptions, we list all possible foliations. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0011-y Issue No:Vol. 48, No. 2 (2017)

Authors:Ricardo Abreu-Blaya; Lianet De la Cruz-Toranzo; Tania R. Gómez-Santiesteban; Yulieth Ramírez-Leyva; Juan Bory-Reyes Pages: 253 - 260 Abstract: In this note, we consider poly-analytic Cauchy integral operators introduced in a rather natural way on the higher order Lipschitz classes. We prove some boundary properties of the function represented by such an integral operator in the general context of rectifiable Jordan curves. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0013-9 Issue No:Vol. 48, No. 2 (2017)

Authors:Aziz El Kacimi Alaoui Pages: 261 - 282 Abstract: Let \(\mathcal{F}\) be a complex foliation by Riemann surfaces defined by a trivial (in the differentiable sense) fibration \(\pi :M\longrightarrow B\) but for which the complex structure on each fibre \(\pi ^{-1}(t)\) may depend on t. Let \(\sigma :B\longrightarrow M\) be a section of \(\pi \) contained in a \(\mathcal{F}\) -relatively compact subset of M. We prove: for any \(\mathcal{F}\) -relatively compact open set U containing \(\Sigma =\sigma (B)\) and any integer \(s\ge 0\) , there exists a function \(U\longrightarrow {\mathbb {C}}\) of class \(C^s\) nonconstant on any leaf of \((U,\mathcal{F})\) , meromorphic along the leaves and whose set of poles is exactly \(\Sigma \) . PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0020-x Issue No:Vol. 48, No. 2 (2017)

Authors:Cícero Carvalho; Victor G. L. Neumann; Hiram H. López Pages: 283 - 302 Abstract: In this paper we introduce a new family of codes, called projective nested cartesian codes. They are obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of \(\mathbb {P}^n(\mathbb {F}_q)\) , and they may be seen as a generalization of the so-called projective Reed–Muller codes. We calculate the length and the dimension of such codes, an upper bound for the minimum distance and the exact minimum distance in a special case (which includes the projective Reed–Muller codes). At the end we show some relations between the parameters of these codes and those of the affine cartesian codes. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0010-z Issue No:Vol. 48, No. 2 (2017)

Authors:Enrique Fernández-Cara; Ivaldo Tributino de Sousa Pages: 303 - 315 Abstract: This paper deals with the local null control of a free-boundary problem for the 1D semilinear heat equation with distributed controls (locally supported in space) or boundary controls (acting at \(x=0\) ). In the main result we prove that, if the final time T is fixed and the initial state is sufficiently small, there exists controls that drive the state exactly to rest at time \(t=T\) . PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0001-0 Issue No:Vol. 48, No. 2 (2017)

Authors:Henrique Vitório Pages: 317 - 333 Abstract: We propose a unified approach to the theory of connections in the geometry of sprays and Finsler metrics which, in particular, gives a simple explanation of the well-known fact that all the classical Finslerian connections provide exactly the same formulas appearing in the calculus of variations. PubDate: 2017-06-01 DOI: 10.1007/s00574-016-0014-8 Issue No:Vol. 48, No. 2 (2017)

Authors:Henrique F. de Lima; Eraldo Lima; Adriano Medeiros; Márcio S. Santos Abstract: We establish Liouville type results concerning two-sided hypersurfaces immersed in a weighted Killing warped product, under suitable constraints either on the Bakry-Émery-Ricci tensor of the base of the ambient space or on the height function of the hypersurface. PubDate: 2017-06-20 DOI: 10.1007/s00574-017-0043-y

Authors:Somorjit Konthoujam Singh; Hemant Kumar Singh; Tej Bahadur Singh Abstract: Let \(G=\mathbb {Z}_p,\) \(p>2\) a prime, act freely on a finitistic space X with mod p cohomology ring isomorphic to that of \(\mathbb {F}P^m\times \mathbb {S}^3\) , where \(m+1\not \equiv 0\) mod p and \(\mathbb {F}=\mathbb {C}\) or \(\mathbb {H}\) . We wish to discuss the nonexistence of G-equivariant maps \(\mathbb {S}^{2q-1}\rightarrow X\) and \( X\rightarrow \mathbb {S}^{2q-1}\) , where \(\mathbb {S}^{2q-1}\) is equipped with a free G-action. These results are analogues of the celebrated Borsuk-Ulam theorem. To establish these results first we find the cohomology algebra of orbit spaces of free G-actions on X. For a continuous map \(f\!:\! X\rightarrow \mathbb {R}^n\) , a lower bound of the cohomological dimension of the partial coincidence set of f is determined. Furthermore, we approximate the size of the zero set of a fibre preserving G-equivariant map between a fibre bundle with fibre X and a vector bundle. An estimate of the size of the G-coincidence set of a fibre preserving map is also obtained. These results are parametrized versions of the Borsuk-Ulam theorem. PubDate: 2017-06-03 DOI: 10.1007/s00574-017-0040-1

Authors:Cícero Aquino; Halyson Baltazar Abstract: The purpose of this article is to study the uniqueness of complete hypersurfaces satisfying some pinching curvature condition. Here, we use the generalized maximum principle of Omori–Yau to obtain uniqueness results for complete spacelike hypersurfaces immersed in a Lorentzian product space. In addition, we obtain the analogue results for complete hypersurfaces immersed in a Riemannian product space. PubDate: 2017-06-02 DOI: 10.1007/s00574-017-0041-0

Authors:Ítalo Melo Abstract: In this paper we will consider the concept of \(\mathbb {P}\) -weakly hyperbolic iterated function systems on compact metric spaces that generalizes the concept of weakly hyperbolic iterated function systems, as defined by Edalat (Inf Comput 124(2):182–197, 1996) and by Arbieto, Santiago and Junqueira (Bull Braz Math Soc New Ser 2016) for a more general setting where the parameter space is a compact metric space. We prove the existence and uniqueness of the invariant measure of a \(\mathbb {P}\) -weakly hyperbolic IFS. Furthermore, we prove an ergodic theorem for \(\mathbb {P}\) -weakly hyperbolic IFS with compact parameter space. PubDate: 2017-05-30 DOI: 10.1007/s00574-017-0042-z

Authors:David A. C. Mollinedo; Christian Olivera Abstract: The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained. The proofs are based on a careful analysis of the associated stochastic flow of characteristics and techniques of stochastic analysis. PubDate: 2017-05-26 DOI: 10.1007/s00574-017-0039-7

Authors:Dante Carrasco-Olivera; Bernardo San Martín Abstract: It is well known that the geometric Lorenz attractor is \(\mathcal {K}^*\) -expansive. In this paper we prove that the Rovella attractor is also \(\mathcal {K}^*\) -expansive in an almost 2-persistent way. PubDate: 2017-05-23 DOI: 10.1007/s00574-017-0038-8

Authors:Masaru Hasegawa; Farid Tari Abstract: The simplest way to have birth of surfaces is through transitions in the fibres of a function f with a Morse singularity of index 0 or 3. It is natural to seek to understand the geometry of newly born surfaces. We consider here the question of finding how many umbilics are on a newly born surface. We show that newly born surfaces in the Euclidean 3-space have exactly 4 umbilic points all of type lemon, provided that the Hessian of f at the singular point has pairwise distinct eigenvalues. This is true in both cases when f is an analytic or a smooth germ. When only two of such eigenvalues are equal, the number of umbilic points is either 2, 4, 6 or 8 when f is an analytic or a generic smooth germ. The same results holds for newly born surfaces in the Minkowski 3-space. In that case when the two eigenvalues associated to the two spacelike eigenvectors are distinct we get exactly 4 umbilic points all of type lemon. If they are equal, the number of umbilic points is either 2, 4, 6 or 8. PubDate: 2017-05-11 DOI: 10.1007/s00574-017-0037-9

Authors:H. Sano; Y. Kabata; J. L. Deolindo Silva; T. Ohmoto Abstract: We present a local classification of smooth surfaces in \({\mathbb {P}}^3\) in terms of the singularity types (of codimension \(\le \) 4) of their central projections to a plane. Based on our classification result, we also give exact normal forms to surface germs at transition moments on bifurcations with respect to parabolic curves and flecnodal curves. PubDate: 2017-04-21 DOI: 10.1007/s00574-017-0036-x

Authors:Angel Cano; Luis Loeza; Alejandro Ucan-Puc Abstract: In this article we show that Bers’ simultaneous uniformization and Köebe’s retrosection theorem do not hold for discrete groups of projective transformations acting on complex projective space. PubDate: 2017-04-13 DOI: 10.1007/s00574-017-0035-y

Authors:Xavier Carvajal; Amin Esfahani; Mahendra Panthee Abstract: Considered in this work is an n-dimensional dissipative version of the Korteweg–de Vries (KdV) equation. Our goal here is to investigate the well-posedness issue for the associated initial value problem in the anisotropic Sobolev spaces. We also study well-posedness behavior of this equation when the dissipative effects are reduced. PubDate: 2017-04-04 DOI: 10.1007/s00574-017-0034-z