Search

In this paper, it is shown that there are infinitely many extremal Beltrami differentials of non-landside type and non-constant modulus in an infinitesimal equivalence class unless the class contains a unique extremal. [ABSTRACT FROM AUTHOR]

Unlike in complex analysis, in all hypercomplex function theories a hypercomplex variable is not monogenic (regular) and there exists a problem to define analogues of positive and negative powers of the complex variable. R. Fueter firstly introduces a system of symmetric regular quaternion polynomials as analogues of positive powers of a complex variable and proves the Taylor theorem in his theory. In Clifford analysis an analogical idea is used. The Fueter symmetric polynomials are both left- and right-regular, the symmetric polynomials in Clifford analysis are also both left- and right-monogenic. In this paper we construct only left-regular quaternion polynomials and show that the theory of regular quaternion functions of a vector valued quaternion variable can be developed using these polynomials. [ABSTRACT FROM AUTHOR]

In this article, we present univalence criteria for polyharmonic and polyanalytic functions. Our approach yields a new criterion for a polyharmonic functions to be fully-accessible. Several examples are presented to illustrate the use of these criteria. [ABSTRACT FROM AUTHOR]

In this paper, we investigate subextension of plurisubharmonic functions in the weighted pluricomplex energy class. Moreover, we show the equality of the weighted Monge–Ampère measures of subextension and the given function. [ABSTRACT FROM PUBLISHER]

We study a recent criterion for the injectivity of a holomorphic curve in, the strong form of which is shown to imply that the image inis auniform surface. This concept is borrowed from geometric function theory in connection with quasidisks. We also obtain a two-point distortion theorem giving sharp estimates for the separation of images in terms of the hyperbolic distance in. [ABSTRACT FROM AUTHOR]