Hausdorff convergence and the limit shape of the unicorns.
Hermite interpolation and an inequality for entire functions of exponential type.
Holomorphic extension of a function whose odd derivatives are summable
Holomorphic Functions with Mean p-valent Derivatives.
Holomorphic motions commuting with semigroups
A holomorphic family , |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms , |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions which, in addition, commute with some holomorphic families of holomorphic endomorphisms of , |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.
Holomorphic solutions of an inhomogeneous Cauchy equation.
Horizontal sections of connections on curves and transcendence
Let K be a number field, X be a smooth projective curve over it and D be a reduced divisor on X. Let (E,∇) be a vector bundle with connection having meromorphic singularities on D. Let and (the ’s may be in the support of D). Using tools from Nevanlinna theory and formal geometry, we give the definition of E-section of arithmetic type of the vector bundle E with respect to the points ; this is the natural generalization of the notion of E-function defined in Siegel-Shidlovskiĭ theory. We prove...
Hyperbolic components of polynomials with a fixed critical point of maximal order
Hyperbolic components of the complex exponential family
We describe the structure of the hyperbolic components of the parameter plane of the complex exponential family, as started in [1]. More precisely, we label each component with a parameter plane kneading sequence, and we prove the existence of a hyperbolic component for any given such sequence. We also compare these sequences with the more commonly used dynamical kneading sequences.
Hyper-order and order of meromorphic functions sharing functions
In this paper we mainly estimate the hyper-order of an entire function which shares one function with its derivatives. Some examples are given to show that the conclusions are meaningful.
Hypertranscendency of conjugacies in complex dynamics.