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

In this paper, we develop topological modules over the ring of bicomplex numbers. We discuss bicomplex convexivity, hyperbolic-valued seminorms and hyperbolic-valued Minkowski functionals in bicomplex modules. We also study the conditions…

We revisit and connect several notions of algebraic multiplicities of zeros of analytic operator-valued functions and discuss the concept of the index of meromorphic operator-valued functions in complex, separable Hilbert spaces.…

Let $f$ be a holomorphic function on the strip $\{z\in C: -\alpha<Im z<\alpha\}, \alpha > 0$, belonging to the class $H(\alpha,-\alpha;\epsilon)$ defined below. It is shown that there exist holomorphic functions $w_1$ on $\{z\in C: 0<Im z…

We review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities…

A definition of hyperbolic meromorphic functions is given and then we discuss the dynamical behavior and the thermodynamic formalism of hyperbolic functions on the Julia set. We prove the important expanding properties for hyperbolic…

Zariski decomposition plays an important role in the theory of algebraic surfaces due to many applications. For irreducible symplectic manifolds Boucksom provided a characterization of his divisorial Zariski decomposition in terms of the…

The existence of the Herman ring of a function adds interest and complexity to the dynamics of the function. We present a detailed and understandable summary of the core discoveries and recent developments on the Herman ring of rational and…

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs.…

The question of whether a closed Riemannian manifold has infinitely many geometrically distinct closed geodesics has a long history. Though unsolved in general, it is well understood in the case of surfaces. For surfaces of revolution…

Let $B^n$ be the $n$-dimensional unit complex ball and let $a$ and $b$ be two distinct points in its closure. Let $f$ be a real-analytic function on the complex unit sphere $\partial B^n.$ Suppose that for any complex line $L,$ meeting the…

We study the homology structure of spaces having an action of the \emph{framed disks} operad. In particular, we compute the relations between Kudo-Araki operations and generalized Batalin-Vilkovisky operators. As an application, we complete…

This treatise investigates holomorphic functions defined on the space of bicomplex numbers introduced by Segre. The theory of these functions is associated with Fueter's theory of regular, quaternionic functions. The algebras of quaternions…

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,…

We present some results on two meromorphic functions from S to the Riemann sphere sharing a number of values where S is a Riemann surface of one of the following types: compact, compact minus finitely many points, the unit disk, a torus,…

This paper studies the uniqueness of two non-integral finite ordered meromorphic functions with finitely many poles when they share two finite sets. Also, studies an answer to a question posed by Gross for a particular class of meromorphic…

The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus $3$ is described in terms of the gradient of it's sigma function. Solutions of corresponding families of polynomial dynamical systems in $\mathbb{C}^4$…

We establish plurisubharmonicity of the envelope of Poisson and Lelong functionals on almost complex manifolds. That is, we generalize the corresponding results for complex manifolds and almost complex manifolds of complex dimension two. We…

The polynomial method has been used recently to obtain many striking results in combinatorial geometry. In this paper, we use affine Hilbert functions to obtain an estimation theorem in finite field geometry. The most natural way to state…

We study rationality properties of geodesic cycle integrals of meromorphic modular forms associated to positive definite binary quadratic forms. In particular, we obtain finite rational formulas for the cycle integrals of suitable linear…

We give a generalization of the Beurling-Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right…