Related papers: Meromorphic Extendibility and the Argument Princip…

Let $f$ be a $C^{1+\alpha}$ diffeomorphism of a compact manifold $M$ preserving a smooth measure $\mu$. We show that if $f:(M,\mu)\to (M,\mu)$ is exponentially mixing then it is Bernoulli.

This work is based on the approach developed by J.~Dorfmeister, F.~Pedit and H.~Wu [GANG and KITCS preprint, Report KITCS94-4-1] to construct maps $\Phi:D\rightarrow R^3$, $D$ being the unit disk in $C$, whose images are surfaces of…

We show that for a compact surface without boundary $M$ the set of cw-expansive homeomorphisms is dense in the set of all the homeomorphisms of $M$ with respect to the $C^0$ topology. After this we show that for a generic homeomorphism $f$…

We prove that the graph of a continuous function $f$, defined on a domain of ${\mathbb C}^n$, is pluripolar if and only if $f$ is holomorphic.

We consider uniqueness results for meromorphic functions $f:{\mathbb C} \to \widehat{\mathbb C}$ such that for certain values $a\in {\mathbb C}$ the implication $f(z)=a \Rightarrow f'(z)=a$ holds, i.e. that $f$ and $f'$ share values {\it…

In this note we prove that a homeomorphism is countably-expansive if and only if it is measure-expansive. This result is applied for showing that the $C^1$-interior of the sets of expansive, measure-expansive and continuum-wise expansive…

The purpose of this article is to show uniqueness theorems for meromorphic mappings of C^m to CP^n with few hyperplanes H_j, j=1,...,q. It is well known that uniqueness theorems hold for q \geq 3n+2. In this paper we show that for every…

We consider the following conjecture (from Huang, et al): Let $\Delta^+$ denote the upper half disc in $\mathbb{C}$ and let $\gamma = ( - 1, 1)$ (viewed as an interval in the real axis in $\mathbb{C}$). Assume that $F$ is a holomorphic…

We prove in this note a result on extension of meromorphic mappings, which can be considered as a direct generalisation of the Hartogs extension theorem for holomorphic functions. Namely: THEOREM. Every meromorphic mapping $f:H_n^q(r)\to…

The main result establishes an estimate for the growth of a real meromorphic function $f$ on the unit disc $\Delta$ such that: (i) at least one of $f$ and $1/f$ has finitely many poles and non-real zeros in $\Delta$; (ii)~$f^{(k)}$ has…

Reidl, S\'anchez Villaamil, and Stravopoulos (2019) characterized graph classes of bounded expansion as follows: A class $\mathcal{C}$ closed under subgraphs has bounded expansion if and only if there exists a function $f:\mathbb{N} \to…

The Brouwer fixed point theorem says that any continuous function from disc to itself has a fixed point. By using simple geometrical technique we have generalized the result in manifold and proved that any continuous function on the…

The problem is considered as to whether a monotone function defined on a subset P of a Euclidean space can be strictly monotonically extended to the whole space. It is proved that this is the case if and only if the function is {\em…

In this paper, we obtain the meromorphic continuation of a q-analogue of multiple zeta function using an elementary formula called translation formula. We then obtain the matrix representation of the translation formula and using it, we…

In this paper, we analyze the theory of meromorphic $(1,0)$-forms $\omega\in\mathcal{M}\Omega^{(1,0)}(\mathbb{CP}^1).$ Hence, we show that on a compact Riemann surface of genus $g=0,$ isomorphic to $\mathbb{CP}^1,$ every non-constant…

A univalent meromorphic function defined on $\Delta:= \{z \in \mathbb{C}: 1<|z|<\infty \}$ with univalent inverse defined on $\Delta$ is bi-univalent meromorphic in $\Delta$. For certain subclasses of meromorphic bi-univalent functions,…

In this paper, we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.

In this article we consider functions $f$ meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions. This condition simplifies and generalizes known conditions. We…

Given a compact of ${\bf R}^n$, there is always a doubling measure having it as its support. We use this fact to construct an integral operator that extends differentiable functions defined on any compact set of ${\bf R}^n$ to the whole of…

We study the pluripolar hull of the graph of a holomorphic function f, defined on a domain D in the complex plane outside a polar set A of D. This leads to a theorem that describes under what conditions f is nowhere extendable over A, while…