Related papers: Bounded meromorphic functions on the complex 2-dis…

This note contains two new theorems about bounded holomorphic functions on the symmetrized bidisk -- a characterization of interpolating sequences and a Toeplitz corona theorem.

This paper has twofold. The first is to establish a second main theorem for meromorphic functions on the complex disc $\Delta (R_0)\subset\mathbb C$ with finite growth index and small functions, where the counting functions are truncated to…

We introduce a class of regular continuous functions on the closed 2-disk and show that each function from this class is topologically conjugate to a linear function defined on a sqare, a closed half-disk or a closed disk.

The purpose of this paper is to develop the theory of holomorphic functions with modulus bounded by $1$ on the symmetrized skew bidisc \[ \mathbb{G}_{r} \stackrel{\rm def}{=} \Big\{( \lambda_{1}+r\lambda_{2} ,r\lambda_{1}\lambda_{2}):…

We discuss meromorphic functions on the complex plane which are Brody curves regarded as holomorphic maps to P_1, i.e., which have bounded spherical derivative.

Let $\mathfrak g$ be an infinite-dimensional Lie algebra, and $G$ be the algebraic completion of a $\mathfrak g$-module. Using the geometric model of Schottky uniformization of Riemann sphere to obtain a higher genus Riemann surface, we…

We prove a new bound on the number of shared values of distinct meromorphic functions on a compact Riemann surface, explain a mistake in a previous paper on this topic, and give a survey of related questions.

We prove that fields of meromorphic functions on Stein surfaces have cohomological dimension 2, and solve the period-index problem and Serre's conjecture II for these fields. We obtain analogous results for fields of real meromorphic…

Let B be the open unit ball in C^2 and let a, b, c be three points in C^2 which do not lie in a complex line, such that the complex line through a and b meets B and such that <a|b> is different from 1 if one of the points a, b is in B and…

Let $\Omega_1,\Omega_2$ be two disjoint open sets in $\mathbf C^n$ whose boundaries share a smooth real hypersurface $M$ as relatively open subsets. Assume that $\Omega_i$ is equipped with a complex structure $J^i$ which is smooth up to…

n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…

We establish plurisubharmonicity of envelopes of certain classical disc functionals on locally irreducible complex spaces, thereby generalizing the corresponding results for complex manifolds. We also find new formulae expressing the…

We classify meromorphic affine connections on compact complex surfaces with algebraic dimension one, extending the work of Inoue,Kobayashi and Ochiai (1981) in the holomorphic case. The motivation is to investigate possible extension of the…

This paper is a continuation of work done in \cite{BS}. It contains two new theorems about bounded holomorphic functions on the symmetrized bidisk -- a characterization of interpolating sequences and a Toeplitz corona theorem.

It is well known that a ramified holomorphic covering of a closed unitary disc by another such a disc is given by a finite Blaschke product. The inverse is also true. In this note we give an explicit description of holomorphic ramified…

We give a full characterization of circle homeomorphisms which admit a homeomorphic extension to the unit disk with finite bi-Sobolev norm. As a special case, a bi-conformal variant of the famous Beurling-Ahlfors extension theorem is…

We prove that the operad of framed little 2-discs is formal. Tamarkin and Kontsevich each proved that the unframed 2-discs operad is formal. The unframed 2-discs is an operad in the category of S^1-spaces, and the framed 2-discs operad can…

The paper contains the proof, in dimension 2, of a conjecture of R. G. Douglas and V. Paulsen concerning the characterization of the ideals of polynomials which are closed in the relative topology induced by the Hardy space of the polydisk.

In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential operations is closed. On basis of these works, we…

We present an extension theorem for a separately holomorphic function which is polynomial/rational in some variables.