Related papers: On critical points of proper holomorphic maps on t…

We prove a result that relates the number of homomorphisms from the fundamental group of a compact nonorientable surface to a finite group $G$, where conjugacy classes of the boundary components of the surface must map to prescribed…

We discuss stationary discs for generic CR manifolds and apply them to the problem of finite jet determination for CR mappings. We prove that a CR diffeomorphism of two finitely smooth strictly pseudoconvex Levi generating CR manifolds is…

We prove Runge-type theorems and universality results for locally univalent holomorphic and meromorphic functions. Refining a result of M. Heins, we also show that there is a universal bounded locally univalent function on the unit disk.…

We study critical points of holomorphic sections of $\ocal(m)$ on $\CP^n$. For quadrics, we give a complete discription of their critical points. When $n=1$, we prove a spherical Gauss-Lucas theorem. For general situation, we prove that a…

We analyze the infinitesimal effect of holomorphic perturbations of the dynamics of a structurally stable rational map on a neighborhood of its Julia set. This implies some restrictions on the behavior of critical points.

Motivated by integral point sets in the Euclidean plane, we consider integral point sets in affine planes over finite fields. An integral point set is a set of points in the affine plane $\mathbb{F}_q^2$ over a finite field $\mathbb{F}_q$,…

We show that if there exists a topologically expansive homeomorphism on a uniform space, then the space is always a regular space. Through examples we show that in general composition of topologically expansive homeomorphisms need not be…

We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of…

We investigate the relationship between the univalence of $f$ and of $h$ in the decomposition $f=h+\bar{g}$ of a sense-preserving harmonic mapping defined in the unit disk $\mathbb{D}\subset\mathbb{C}$. Among other results, we determine the…

We extend a theorem of Herman from the case of unicritical polynomials to the case of polynomials with two finite critical values. This theorem states that Siegel disks of such polynomials, under a diophantine condition (called Herman's…

Biharmonic and conformal-biharmonic maps are two fourth-order generalizations of the well-studied notion of harmonic maps in Riemannian geometry. In this article we consider maps into the Euclidean sphere and investigate a geometric…

We define the generalized logarithmic Gauss map for algebraic varieties of the complex algebraic torus of any codimension. Moreover, we describe the set of critical points of the logarithmic mapping restricted to our variety, and we show an…

In this study, we derive the sharp bounds of certain Toeplitz determinants whose entries are the coefficients of holomorphic functions belonging to a class defined on the unit disk $\mathbb{U}$. Further, these results are extended to a…

We characterize two classical types of conformality of a holomorphic self-map of the unit disk at a boundary point - existence of a finite angular derivative in the sense of Carath\'eodory and the weaker property of angle preservation - in…

We prove that $i)$ if $\mathcal{A}$ is $\lambda $-accessible and it is axiomatizable in (finitary) coherent logic then $\lambda $-pure maps are strict monomorphisms and $ii)$ if there is a proper class of strongly compact cardinals and…

We investigate the critical points of the basic (quasi-)modular forms $E_2$, $E_4$, and $E_6$. They occur where some associated polymorphic functions have poles. By an explicit description of these polymorphic functions as conformal maps,…

We prove that strong finite total curvature complete hypersurfaces of (n+1)-euclidean space are proper and diffeomorphic to a compact manifold minus finitely many points. With an additional condition, we also prove that the Gauss map of…

We study proper holomorphic maps of annuli in complex Euclidean spaces, that is, domains with $U(n)$ as the automorphism group. By the Hartogs phenomenon and a result of Forstneri\v{c}, such maps are always rational and extend to proper…

We consider the space of holomorphic maps from a compact Riemann surface to a projective space blown up at finitely many points. We show that the homology of this mapping space equals that of the space of continuous maps that intersect the…

We construct certain non-degenerate maps and sets, mainly in the complex-analytic category. For example, we show that for every countable subset S in an irreducible complex space X there exists a holomorphic map from the unit disk to X such…