复变函数

We give a general construction of entire functions in $d$ complex variables that vanish on a lattice of the form $L = A (Z + i Z )^d$ for an invertible complex-valued matrix. As an application we exhibit a class of lattices of density >1…

The paper is devoted to study the uniqueness problem of linear delay-differential operator of a meromorphic function sharing two sets or small function together with values with its $c$-shift and $q$-shift operator. Results of this paper…

In the paper, we discuss how it would be possible to succeed in Stahl's novel approach, 1987--1988, to explore Hermite--Pad\'e polynomials based on Riemann surface properties. In particular, we explore the limit zero distribution of type I…

We observe that a recent result by Gardiner and Sj\"odin, solving a problem of Kr\'{a}l on subharmonic functions, can be easily generalized to yield a somewhat stronger result. This can be combined with a viscosity technique of ours, which…

We prove that a conformal mapping defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the harmonic measure converge. With the aid of this theorem, we give a geometric characterization of…

Based on a well known Sh.-T. Yau theorem we obtain that the real part of a holomorphic function on a K\"{a}hler manifold with the Ricci curvature bounded from below by $-1$ is contractive with respect to the distance on the manifold and the…

Let $\{f_\nu\}$ be a sequence of holomorphic self-maps of a hyperbolic Riemann surface $X$. In this paper we shall study the asymptotic behavior of the sequences obtained by iteratively left-composing or right-composing the maps…

For an entire function $f(z) = \sum_{k=0}^\infty a_k z^k,$ $a_k >0,$ we define the sequence of the second quotients of Taylor coefficients $Q := \left( \frac{a_k^2}{a_{k-1}a_{k+1}} \right)_{k=1}^\infty$. We find new necessary conditions for…

In this note, we investigate some regularity aspects for solutions of degenerate complex Monge-Amp\`ere equations (DCMAE) on singular spaces. First, we study the Dirichlet problem for DCMAE on singular Stein spaces, showing a general…

By establishing a unified estimate of the twisted Kohn-Morrey-H\"{o}rmander estimate and the $q$-pseudoconvex Ahn-Zampieri estimate, we discuss variants of Property $(P_q)$ of Catlin and Property $(\widetilde{P_q})$ of McNeal on the…

We consider the Dirichlet problem for the Beltrami equation in some simply connected domain. We consider the class of all homeomorphic solutions of such a problem with a normalization condition and set-theoretic constraints on their complex…

In this article we obtain large deviation estimates for zeros of random holomorphic sections on punctured Riemann surfaces. These estimates are then employed to yield estimates for the respective hole probabilities. A particular case of…

We continue the research on the structure of complex geodesics in tube domains over (bounded) convex bases. In some special cases a more explicit form of the geodesics than the existing ones are provided. As one of the consequences of our…

Consider a very ample line bundle $ E \to X$ over a compact complex manifold, endowed with a hermitian metric of curvature $-i \omega $, and the space $\mathcal{O}(E)$ of its holomorphic sections. The Fubini--Study map associates with…

In the slice Hardy space over the unit ball of quaternions, we introduce the slice hyperbolic backward shift operator $\mathcal S_a$ with the decomposition process $$f=e_a\langle f, e_a\rangle+B_{a}*\mathcal S_a f,$$ where $e_a$ denotes the…

We investigate the construction of real analytic Levi-flat hypersurfaces in K3 surfaces. By taking images of real hyperplanes, one can construct such hypersurfaces in two-dimensional complex tori. We show that "almost every" K3 surfaces…

In this paper we investigate a topological characterization of the Runge theorem in the Clifford algebra $ \mathbb{R}_3$ via the description of the homology groups of axially symmetric open subsets of the quadratic cone in $\mathbb{R}_3$.

We prove the continuity of logarithmic capacity under Hausdorff convergence of uniformly perfect planar sets. The continuity holds when the Hausdorff distance to the limit set tends to zero at sufficiently rapid rate, compared to the decay…

An inverse problem of elasticity of $n$ elastic inclusions embedded into an elastic half-plane is analyzed. The boundary of the half-plane is free of traction. The half-plane and the inclusions are subjected to antiplane shear, and the…

We prove that the homogeneously polyanalytic functions of total order $m$, defined by the system of equations $\overline{D}^{(k_1,\ldots,k_n)} f=0$ with $k_1+\cdots+k_n=m$, can be written as polynomials of total degree $<m$ in variables…