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Homology of origamis with symmetries

Carlos Matheus, Jean-Christophe Yoccoz, David Zmiaikou (2014)

Annales de l’institut Fourier

Given an origami (square-tiled surface) M with automorphism group Γ , we compute the decomposition of the first homology group of M into isotypic Γ -submodules. Through the action of the affine group of M on the homology group, we deduce some consequences for the multiplicities of the Lyapunov exponents of the Kontsevich-Zorich cocycle. We also construct and study several families of interesting origamis illustrating our results.

Hörmander systems and harmonic morphisms

Elisabetta Barletta (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Given a Hörmander system X = { X 1 , ⋯ , X m } on a domain Ω ⊆ 𝐑 n we show that any subelliptic harmonic morphism φ from Ω into a ν -dimensional riemannian manifold N is a (smooth) subelliptic harmonic map (in the sense of J. Jost & C-J. Xu, [9]). Also φ is a submersion provided that ν ≤ m and X has rank m . If Ω = 𝐇 n (the Heisenberg group) and X = 1 2 L α + L α ¯ , 1 2 i L α - L α ¯ , where L α ¯ = ∂ / ∂ z ¯ α - i z α ∂ / ∂ t is the Lewy operator, then a smooth map φ : Ω → N is a subelliptic harmonic morphism if and only if φ ∘ π : ( C ( 𝐇 n ) , F θ 0 ) → N is a harmonic morphism, where S 1 → C ( 𝐇 n ) → π → 𝐇 n is the canonical circle bundle and F θ 0 is the Fefferman...

Hua-harmonic functions on symmetric type two Siegel domains

Dariusz Buraczewski, Ewa Damek (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study a natural system of second order differential operators on a symmetric Siegel domain D that is invariant under the action of biholomorphic transformations. If D is of type two, the space of real valued solutions coincides with pluriharmonic functions. We show the main idea of the proof and give a survey of previous results.

Hulls of subsets of the torus in ℂ 2

Herbert Alexander (1998)

Annales de l'institut Fourier

We construct a non-polynomially convex compact subset of the unit torus in ℂ 2 with polynomially convex hull containing no analytic structure.

Hyperbolic Cauchy problem and Leray's residue formula

Susumu Tanabé (2000)

Annales Polonici Mathematici

We give an algebraic description of (wave) fronts that appear in strictly hyperbolic Cauchy problems. A concrete form of a defining function of the wave front issued from the initial algebraic variety is obtained with the aid of Gauss-Manin systems satisfied by Leray's residues.

Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

Apostolova, Lilia N. (2012)

Mathematica Balkanica New Series

MSC 2010: 30C10, 32A30, 30G35The algebra R(1; j; j2; j3), j4 = ¡1 of the fourth-R numbers, or in other words the algebra of the double-complex numbers C(1; j) and the corresponding functions, were studied in the papers of S. Dimiev and al. (see [1], [2], [3], [4]). The hyperbolic fourth-R numbers form other similar to C(1; j) algebra with zero divisors. In this note the square roots of hyperbolic fourth-R numbers and hyperbolic complex numbers are found. The quadratic equation with hyperbolic fourth-R...

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