On first order elliptic equations for sections of complex line bundles
Using a result due to M. Shub, a theorem about the existence of fixed points inside the unit disc for extensions of expanding maps defined on the boundary is established. An application to a special class of rational maps on the Riemann sphere and some considerations on ergodic properties of these maps are also made.
A criterion for the existence of fixed point of one-dimensional holomorphic maps is established.
The paper concerns properties of holomorphic functions satisfying more than one equation of Schiffer type (-equation). Such equations are satisfied, in particular, by functions that are extremal (in various classes of univalent functions) with respect to functionals depending on a finite number of coefficients.
One of the basic questions in the Kleinian group theory is to understand both algebraic and geometric limiting behavior of sequences of discrete subgroups. In this paper we consider the geometric convergence in the setting of the isometric group of the real or complex hyperbolic space. It is known that if is a non-elementary finitely generated group and a sequence of discrete and faithful representations, then the geometric limit of is a discrete subgroup of . We generalize this result by...
By using the properties of convergence and global smoothness preservation of multivariate Weierstrass singular integrals, we establish multivariate complex Carleman type approximation results with rates. Here the approximants fulfill the global smoothness preservation property. Furthermore Mergelyan's theorem for the unit disc is strengthened by proving the global smoothness preservation property.