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1. CJM Online first

Andrade, Jaime; Dávila, Nestor; Pérez-Chavela, Ernesto; Vidal, Claudio
 Dynamics and regularization of the Kepler problem on surfaces of constant curvature We classify and analyze the orbits of the Kepler problem on surfaces of constant curvature (both positive and negative, $\mathbb S^2$ and $\mathbb H^2$, respectively) as function of the angular momentum and the energy. Hill's region are characterized and the problem of time-collision is studied. We also regularize the problem in Cartesian and intrinsic coordinates, depending on the constant angular momentum and we describe the orbits of the regularized vector field. The phase portrait both for $\mathbb S^2$ and $\mathbb H^2$ are pointed out. Keywords:Kepler problem on surfaces of constant curvature, Hill's region, singularities, regularization, qualitative analysis of ODECategories:70F16, 70G60

2. CJM Online first

Garbagnati, Alice
 On K3 surface quotients of K3 or Abelian surfaces The aim of this paper is to prove that a K3 surface is the minimal model of the quotient of an Abelian surface by a group $G$ (respectively of a K3 surface by an Abelian group $G$) if and only if a certain lattice is primitively embedded in its NÃ©ron-Severi group. This allows one to describe the coarse moduli space of the K3 surfaces which are (rationally) $G$-covered by Abelian or K3 surfaces (in the latter case $G$ is an Abelian group). If either $G$ has order 2 or $G$ is cyclic and acts on an Abelian surface, this result was already known, so we extend it to the other cases. Moreover, we prove that a K3 surface $X_G$ is the minimal model of the quotient of an Abelian surface by a group $G$ if and only if a certain configuration of rational curves is present on $X_G$. Again this result was known only in some special cases, in particular if $G$ has order 2 or 3. Keywords:K3 surfaces, Kummer surfaces, Kummer type lattice, quotient surfacesCategories:14J28, 14J50, 14J10

3. CJM 2015 (vol 68 pp. 24)

Bonfanti, Matteo Alfonso; van Geemen, Bert
 Abelian Surfaces with an Automorphism and Quaternionic Multiplication We construct one dimensional families of Abelian surfaces with quaternionic multiplication which also have an automorphism of order three or four. Using Barth's description of the moduli space of $(2,4)$-polarized Abelian surfaces, we find the Shimura curve parametrizing these Abelian surfaces in a specific case. We explicitly relate these surfaces to the Jacobians of genus two curves studied by Hashimoto and Murabayashi. We also describe a (Humbert) surface in Barth's moduli space which parametrizes Abelian surfaces with real multiplication by $\mathbf{Z}[\sqrt{2}]$. Keywords:abelian surfaces, moduli, shimura curvesCategories:14K10, 11G10, 14K20

4. CJM 2012 (vol 65 pp. 621)

Lee, Paul W. Y.
 On Surfaces in Three Dimensional Contact Manifolds In this paper, we introduce two notions on a surface in a contact manifold. The first one is called degree of transversality (DOT) which measures the transversality between the tangent spaces of a surface and the contact planes. The second quantity, called curvature of transversality (COT), is designed to give a comparison principle for DOT along characteristic curves under bounds on COT. In particular, this gives estimates on lengths of characteristic curves assuming COT is bounded below by a positive constant. We show that surfaces with constant COT exist and we classify all graphs in the Heisenberg group with vanishing COT. This is accomplished by showing that the equation for graphs with zero COT can be decomposed into two first order PDEs, one of which is the backward invisicid Burgers' equation. Finally we show that the p-minimal graph equation in the Heisenberg group also has such a decomposition. Moreover, we can use this decomposition to write down an explicit formula of a solution near a regular point. Keywords:contact manifolds, subriemannian manifolds, surfacesCategory:35R03

5. CJM 2010 (vol 62 pp. 1201)

Alzati, Alberto; Besana, Gian Mario
 Criteria for Very Ampleness of Rank Two Vector Bundles over Ruled Surfaces Very ampleness criteria for rank $2$ vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low degree. Keywords:vector bundles, very ampleness, ruled surfacesCategories:14E05, 14J30

6. CJM 1999 (vol 51 pp. 470)

Bshouty, D.; Hengartner, W.
 Exterior Univalent Harmonic Mappings With Finite Blaschke Dilatations In this article we characterize the univalent harmonic mappings from the exterior of the unit disk, $\Delta$, onto a simply connected domain $\Omega$ containing infinity and which are solutions of the system of elliptic partial differential equations $\fzbb = a(z)f_z(z)$ where the second dilatation function $a(z)$ is a finite Blaschke product. At the end of this article, we apply our results to nonparametric minimal surfaces having the property that the image of its Gauss map is the upper half-sphere covered once or twice. Keywords:harmonic mappings, minimal surfacesCategories:30C55, 30C62, 49Q05
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