Search results for "Geometric"
showing 10 items of 652 documents
A Laplace type problem for a lattice with cell composed by two trapezius and a triangle
2014
In the previous papers, [1], [2], [3], [4], [5], [6], [7], [8], [9] and [10] the authors study some Laplace problem for different lattices. In this paper we determine the probability that a random segment of constant length intersects a side of lattice with cell represented in fig.1
Theta-characteristics on singular curves
2007
On a smooth curve a theta–characteristic is a line bundle L with square that is the canonical line bundle ω. The equivalent conditionHom(L, ω) ∼= L generalizes well to singular curves, as applications show. More precisely, a theta–characteristic is a torsion–free sheaf F of rank 1 with Hom(F , ω) ∼= F . If the curve has non ADE–singularities then there are infinitely many theta–characteristics. Therefore, theta–characteristics are distinguished by their local type. The main purpose of this article is to compute the number of even and odd theta–characteristics (i.e. F with h(C,F) ≡ 0 resp. h(C,F) ≡ 1 modulo 2) in terms of the geometric genus of the curve and certain discrete invariants of a …
Un exemple de flot d'Anosov transitif transverse à un tore et non conjugué à une suspension
1994
AbstractWe construct an example of transitive Anosov flow on a compact 3-manifold, which admits a transversal torus and is not the suspension of an Anosov diffeomorphism.
The horospherical Gauss-Bonnet type theorem in hyperbolic space
2006
We introduce the notion horospherical curvatures of hypersurfaces in hyperbolic space and show that totally umbilic hypersurfaces with vanishing cur- vatures are only horospheres. We also show that the Gauss-Bonnet type theorem holds for the horospherical Gauss-Kronecker curvature of a closed orientable even dimensional hypersurface in hyperbolic space. + (i1) by using the model in Minkowski space. We introduced the notion of hyperbolic Gauss indicatrices slightly modified the definition of hyperbolic Gauss maps. The notion of hyperbolic indicatrices is independent of the choice of the model of hyperbolic space. Using the hyperbolic Gauss indicatrix, we defined the principal hyperbolic curv…
Sobolev homeomorphic extensions onto John domains
2020
Abstract Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the classical Jordan-Schoenflies theorem may admit no solution - it is possible to have a boundary homeomorphism which admits a continuous W 1 , 2 -extension but not even a homeomorphic W 1 , 1 -extension. We prove that if the target is assumed to be a John disk, then any boundary homeomorphism from the unit circle admits a Sobolev homeomorphic extension for all exponents p 2 . John disks, being one sided quasidisks, are of fundamental importance in Geometric Function The…
Coordinates for quasi-Fuchsian punctured torus space
1998
We consider complex Fenchel-Nielsen coordinates on the quasi-Fuchsian space of punctured tori. These coordinates arise from a generalisation of Kra's plumbing construction and are related to earthquakes on Teichmueller space. They also allow us to interpolate between two coordinate systems on Teichmueller space, namely the classical Fuchsian space with Fenchel-Nielsen coordinates and the Maskit embedding. We also show how they relate to the pleating coordinates of Keen and Series.
A note on the unirationality of a moduli space of double covers
2010
In this note we look at the moduli space $\cR_{3,2}$ of double covers of genus three curves, branched along 4 distinct points. This space was studied by Bardelli, Ciliberto and Verra. It admits a dominating morphism $\cR_{3,2} \to {\mathcal A}_4$ to Siegel space. We show that there is a birational model of $\cR_{3,2}$ as a group quotient of a product of two Grassmannian varieties. This gives a proof of the unirationality of $\cR_{3,2}$ and hence a new proof for the unirationality of ${\mathcal A}_4$.
Arithmeticity of Four Hypergeometric Monodromy Groups Associated to Calabi–Yau Threefolds: Table 1.
2014
In [12], we show that three of the fourteen hypergeometric monodromy groups associated to Calabi-Yau threefolds are arithmetic. Brav-Thomas (in [3]) show that seven of the remaining eleven are thin. In this article, we settle the arithmeticity problem for the fourteen monodromy groups, by showing that, the remaining four are arithmetic.
On BLD-mappings with small distortion
2021
We show that every $$L$$ -BLD-mapping in a domain of $$\mathbb {R}^{n}$$ is a local homeomorphism if $$L < \sqrt{2}$$ or $$K_I(f) < 2$$ . These bounds are sharp as shown by a winding map.
Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
2015
We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the first kind. The coefficients of different expansions obey four-, five-, or six-term recurrence relations that are reduced to ones involving less number of terms only in a few exceptional cases. The conditions for deriving finite-sum solutions via termination of the series are discussed.