复变函数

We study the chordal Loewner equation associated with certain driving functions that produce infinitely many slits. Specifically, for a choice of a sequence of positive numbers $(b_n)_{n\ge1}$ and points of the real line $(k_n)_{n\ge1}$, we…

The purpose of the present paper is to investigate $G$-opers on pointed Riemann surfaces (for a simple algebraic group $G$ of adjoint type) and their monodromy maps. In the first part, we review some general facts on $G$-opers, or more…

Let $X$ be a compact subset of the complex plane and $x \in X$. A necessary and sufficient condition is given in terms of Hausdorff contents for the existence of a bounded point derivation at $x$ on the space of vanishing Campanato…

Let $X$ be a compact K\"ahler manifold of complex dimension $k\ge 2$ and $f:X\to X$ a surjective holomorphic endomorphism of simple action on cohomology. We prove that the sequence of normalized pull-backs of a non-pluripolar current under…

In this paper, we obtain the sharp bounds of the second Hankel determinant of logarithmic inverse coefficients for the strongly starlike and strongly convex functions of order alpha.

Given a complete K\"ahler manifold $(X,\,\omega)$ with finite second Betti number, a smooth complex hypersurface $Y\subset X$ and a smooth real $d$-closed $(1,\,1)$-form $\alpha$ on $X$ with arbitrary, possibly non-rational, De Rham…

In this paper, we discuss meromorphic solutions of functional equations over non-Archimedean fields, and prove analogues of the Clunie lemma, Malmquist-type theorem and Mokhon'ko theorem.

In this paper, the order boundedness and essential norm of generalized weighted composition operators on Bergman spaces with doubling weights are characterized. Specially, we estimate the essential norm of these operators on weighted…

This paper has two parts. We first survey recent efforts on the Bloom conjecture which still remains open in the case of complex dimension at least 4. Bloom's conjecture concerns the equivalence of three regular types. There is a more…

In a recent preprint published on arXiv (see arXiv:2308.02993v2, referred here as \cite{NXH}), N.X. Hong stated that every plurifinely open set $U\subset \mathbb{C}^n$, $n\geq 1$, is of the form $U=\bigcup \{\varphi_j>-1\}$, where each…

This paper primarily concerns the variance estimate of zeros of systems of random holomorphic sections associated with a sequence of smooth Hermitian holomorphic line bundles on a compact Kahler manifold X. The probability measures taken…

We introduce the notion of an ``RR-space''. (RR stands for Rosay and Rudin.) These spaces essentially share the properties of tame subsets known for ${\bf C}^n$. The class of RR-spaces contains character-free complex linear algebraic groups…

We study Clark measures on the unit polydisc, giving an overview of recent research and investigating the Clark measures of some new examples of multivariate inner functions. In particular, we study the relationship between Clark measures…

The Sendov conjecture asserts that if $p(z) = \prod_{j=1}^{N}(z-z_j)$ is a polynomial with zeros $|z_j| \leq 1$, then each disk $|z-z_j| \leq 1$ contains a zero of $p'$. Our purpose is the following: Given a zero $z_j$ of order $n \geq 2$,…

The Wong-Rosay theorem characterizes the strongly pseudoconvex domains of $\mathbb{C}^n$ by their automorphism groups. It has a lot of generalizations to other kinds of domains (for example, the weakly pseudoconvex domains). However, most…

The aim of the paper is to investigate the structure of plurifinely open sets. As an application, we will prove an equality on complex Monge-Amp\`ere measures in plurifinely open sets.

The moduli space of projective structures on a compact oriented surface $\Sigma$ has a holomorphic symplectic structure, which is constructed by pulling back, using the monodromy map, the Atiyah--Bott--Goldman symplectic form on the…

We prove that frame set $\mathcal{F}_g$ for imaginary shift of sinc-function $$g(t)=\frac{\sin\pi b(t-iw)}{t-iw}, \quad b,w\in\mathbb{R}\setminus\{0\}$$ can be described as $\mathcal{F}_g=\{(\alpha,\beta): \alpha\beta\leq 1,…

In this manuscript we systematically review known results of local dynamics of discrete local holomorphic dynamics near fixed points in one and several complex variables as well as the consequences in global dynamics.

In this article, we study some properties of the $n$-th order weighted reduced Bergman kernels for planar domains, $n\geq 1$. Specifically, we look at Ramadanov type theorems, localization, and boundary behaviour of the weighted reduced…