相关论文: Mapping properties of analytic functions on the di…

Estimates are obtained for the initial coefficients of a normalized analytic function $f$ in the unit disk $\mathbb{D}$ such that $f$ and the analytic extension of $f^{-1}$ to $\mathbb{D}$ belong to certain subclasses of univalent…

We study biorthogonal sequences with special properties, such as weak or weak-star convergence to 0, and obtain an extension of the Josefson-Nissenzweig theorem. This result is applied to embed analytic disks in the fiber over 0 of the…

The convolution properties are discussed for the complex-valued harmonic functions in the unit disk $\mathbb{D}$ constructed from the harmonic shearing of the analytic function $\phi(z):=\int_0^z…

In this note, we mainly concern the set $U_f$ of $c\in\mathbb{C}$ such that the power deformation $z(f(z)/z)^c$ is univalent in the unit disk $|z|<1$ for a given analytic univalent function $f(z)=z+a_2z^2+\cdots$ in the unit disk. We will…

This article contains several results for \lambda-Robertson functions, i.e., analytic functions $f$ defined on the unit disk $D$ satisfying $f(0) = f'(0)-1=0$ and $Re e^{-i\lambda} {1+zf"(z)/f'(z)} > 0$ in $D$, where $\lambda \epsilon…

A normalized univalent function is uniformly convex if it maps every circular arc contained in the open unit disk with center in it into a convex curve. This article surveys recent results on the class of uniformly convex functions and on…

In the present paper, we obtain a more general conditions for univalence of analytic functions in the open unit disk U. Also, we obtain a refinement to a quasiconformal extension criterion of the main result.

In this paper, we present a function-sharing criterion for the normality of meromorphic functions. Let $f$ be a meromorphic function in the unit disc $\mathbb{D}\subset \mathbb{C}$, $\psi_1$, $\psi_2$, and $\psi_3$ be three meromorphic…

We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and the other one is a generalized Mathieu type power series involving factorials in its coefficients.…

Let $M\subset S^{n+1}\subset\mathbb{R}^{n+2}$ be a compact minimal hypersurface of the $n$-dimensional Euclidean unit sphere. Let us denote by $|A|^2$ the square of the norm of the second fundamental form and $J(f)=-\Delta f-nf-|A|^2f$ the…

We find the radius of starlikeness of order $\alpha$, $0\leq \alpha<1$, of normalized analytic functions $f$ on the unit disk satisfying either $\operatorname{Re}(f(z)/g(z))>0$ or $\left| (f(z)/g(z))-1\right|<1$ for some close-to-star…

Given a set ${\cal D}$ of unit disks in the Euclidean plane, we consider (i) the {\it discrete unit disk cover} (DUDC) problem and (ii) the {\it rectangular region cover} (RRC) problem. In the DUDC problem, for a given set ${\cal P}$ of…

In this article we consider a family $\mathcal{C}(A, B)$ of analytic and locally univalent functions on the open unit disc $\ID=\{z :|z|<1\}$ in the complex plane that properly contains the well-known Janowski class of convex univalent…

We study the Reidemeister torsion and the analytic torsion of the $m$ dimensional disc in the Euclidean $m$ dimensional space, using the base for the homology defined by Ray and Singer in \cite{RS}. We prove that the Reidemeister torsion…

We find a relationship between the partition function mass zeros and the spectral properties of the QCD Dirac operator in the context of chiral Random Matrix Theory. Introducing the concept of normal modes we see that certain features of…

If $\mathcal{G}$ is the group (under composition) of diffeomorphisms $f : {\bar{D}}(0;1) \rightarrow {\bar{D}}(0;1)$ of the closed unit disc ${\bar{D}}(0;1)$ which are the identity map $id : {\bar{D}}(0;1) \rightarrow {\bar{D}}(0;1)$ on the…

If a function $f$, acting on a Euclidean space $\mathbb{R}^n$, is "almost" orthogonally additive in the sense that $f(x+y)=f(x)+f(y)$ for all $(x,y)\in\bot\setminus Z$, where $Z$ is a "negligible" subset of the $(2n-1)$-dimensional manifold…

Let $f$ be a meromorphic univalent function on the open unit disk having a simple pole at $p\in (0,1)$ that extends continuously to the left half $\IT^{-}$ of the unit circle. In this article, we prove that the ratio of the length of the…

We show that every finite-dimensional Euclidean space contains compact universal differentiability sets of upper Minkowski dimension one. In other words, there are compact sets $S$ of upper Minkowski dimension one such that every Lipschitz…

If there is a topologically locally constant family of smooth algebraic varieties together with an admissible normal function on the total space, then the latter is constant on any fiber if this holds on some fiber. Combined with spreading…