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Hyperbolic measure of maximal entropy for generic rational maps of ℙ k

Gabriel Vigny (2014)

Annales de l’institut Fourier

Let f be a dominant rational map of ℙ k such that there exists s < k with λ s ( f ) > λ l ( f ) for all l . Under mild hypotheses, we show that, for A outside a pluripolar set of Aut ( ℙ k ) , the map f ∘ A admits a hyperbolic measure of maximal entropy log λ s ( f ) with explicit bounds on the Lyapunov exponents. In particular, the result is true for polynomial maps hence for the homogeneous extension of f to ℙ k + 1 . This provides many examples where non uniform hyperbolic dynamics is established.One of the key tools is to approximate the graph of a meromorphic...

Hyperbolic spaces in Teichmüller spaces

Christopher J. Leininger, Saul Schleimer (2014)

Journal of the European Mathematical Society

We prove, for any n , that there is a closed connected orientable surface S so that the hyperbolic space ℍ n almost-isometrically embeds into the Teichmüller space of S , with quasi-convex image lying in the thick part. As a consequence, ℍ n quasi-isometrically embeds in the curve complex of S .

Hyperbolicity and integral points off divisors in subgeneral position in projective algebraic varieties

Do Duc Thai, Nguyen Huu Kien (2015)

Acta Arithmetica

The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety V ⊂ ℙ k ̅ m , where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety V ⊂ ℙ ℂ m .

Hyperbolic-like manifolds, geometrical properties and holomorphic mappings

Grzegorz Boryczka, Luis Tovar (1996)

Banach Center Publications

The authors are dealing with the Dirichlet integral-type biholomorphic-invariant pseudodistance ρ X α ( z 0 , z ) [ ] introduced by Dolbeault and Ławrynowicz (1989) in connection with bordered holomorphic chains of dimension one. Several properties of the related hyperbolic-like manifolds are considered remarking the analogies with and differences from the familiar hyperbolic and Stein manifolds. Likewise several examples are treated in detail.

Hyperconvexity of non-smooth pseudoconvex domains

Xu Wang (2014)

Annales Polonici Mathematici

We show that a bounded pseudoconvex domain D ⊂ ℂⁿ is hyperconvex if its boundary ∂D can be written locally as a complex continuous family of log-Lipschitz curves. We also prove that the graph of a holomorphic motion of a bounded regular domain Ω ⊂ ℂ is hyperconvex provided every component of ∂Ω contains at least two points. Furthermore, we show that hyperconvexity is a Hölder-homeomorphic invariant for planar domains.

Hypercyclicity of convolution operators on spaces of entire functions

F.J. Bertoloto, G. Botelho, V.V. Fávaro, A.M. Jatobá (2013)

Annales de l’institut Fourier

In this paper we use Nachbin’s holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables

Hyperelliptic action integral

Bernhard Elsner (1999)

Annales de l'institut Fourier

Applying the “exact WKB method” (cf. Delabaere-Dillinger-Pham) to the stationary one-dimensional Schrödinger equation with polynomial potential, one is led to a multivalued complex action-integral function. This function is a (hyper)elliptic integral; the sheet structure of its Riemann surface above the plane of its values has interesting properties: the projection of its branch-points is in general a dense subset of the plane, and there is a group of symmetries acting on the surface. The distribution...

Hyperholomorphic connections on coherent sheaves and stability

Misha Verbitsky (2011)

Open Mathematics

Let M be a hyperkähler manifold, and F a reflexive sheaf on M. Assume that F (away from its singularities) admits a connection ▿ with a curvature Θ which is invariant under the standard SU(2)-action on 2-forms. If Θ is square-integrable, such sheaf is called hyperholomorphic. Hyperholomorphic sheaves were studied at great length in [21]. Such sheaves are stable and their singular sets are hyperkähler subvarieties in M. In the present paper, we study sheaves admitting a connection with SU(2)-invariant...

Hyperplane arrangements and Milnor fibrations

Alexander I. Suciu (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank 1 local systems on the complement of the arrangement to gain information on the homology of the other three spaces, and on the monodromy operators of the various fibrations.

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