Results 221 to 230 of about 68,847 (256)

Extremal problems in geometric function theory

Russian Mathematical Surveys, 2023
This survey is devoted to a number of achievements in the theory of extremal problems in geometric function theory. The approaches to the solution of problems under consideration and the methods used are based on conformal isomorphisms and on the theory of univalent functions developed since the beginning of the 20th century.
Avkhadiev, Farit G., Kayumov, Ilgiz R., Nasyrov, Semen R.   +2 more
openaire   +2 more sources

Theory of geometric generating functionals

Classical and Quantum Gravity, 1992
A geometrical and background field-dependent definition of the off-shelf effective action is considered, in the context of a theory of geometric generating functionals, which is based on a linear coupling with an external source J. The only requirements are geometry and a set of minimal properties related to the usefulness of the effective action.
H E Camblong, C R Ordonez
openaire   +1 more source

The Geometric Theory of Holomorphic Functions

1999
The main objects of study in this chapter are holomorphic functions h: U→ V, with U and V open in ℂ, that are one-to-one and onto. Such a holomorphic function is called a conformal (or biholomorphic) mapping. The fact that h is supposed to be one-to-one implies that h’ is nowhere zero on U [remember that if h’ vanishes to order k ≥ 0 at a point P ∈ U ...
openaire   +1 more source

The Geometric Theory of Harmonic Functions

1981
Consider the transformation on the complex plane $$ w = \frac{{z - a}}{{1 - \bar az}},\,\,\,\,\,\left| a \right|\,\, < \,1, $$ (1) where \( \bar a \) denotes the conjugate of a, and the transformation $$ w = {e^{i\theta }}z. $$ (2) From (1) it follows that $$ 1 - {\left| w \right|^2} = 1 - \frac{{(z - a)(\bar z - \bar a)}}{{(1 -
openaire   +1 more source

Discrete geometric function theory II

Applicable Analysis, 1979
The foundations are laid here for a discrete analytic function theory which can be applied to geometric difference (or q-difference) functions. Using the concept of a q-analytic function. a discrete contour integral is defined and analogues are found for Cauchy integral theorems.
C. J. Harman, R. J. Duffin
openaire   +1 more source

Special Functions in Geometric Function Theory

2005
Qiu, S., Vuorinen, M.
openaire   +3 more sources

Linear Methods in Geometric Function Theory

The American Mathematical Monthly, 1985
(1985). Linear Methods in Geometric Function Theory. The American Mathematical Monthly: Vol. 92, No. 6, pp. 392-406.
openaire   +1 more source

Geometric theory of G-functions.

1997
Our object of study are G-connections i.e. linear partial differential equations satisfied by G-functions in several variables [A], [DGS]; typical examples are non-confluent generalized hypergeometric connections with rational parameters [GHF, Chap. 12]. Our main result is the stability of this notion under higher direct images, for any smooth morphism.
ANDRE' Y., BALDASSARRI, FRANCESCO
openaire   +1 more source

Geometric function theory over quaternionic slice domains

Journal of Mathematical Analysis and Applications, 2021
Caterina Stoppato, Graziano Gentili
exaly  

Methods of geometric function theory. II

In these two survey papers the author provides an overview of the methods of geometric function theory. Each paper is dedicated to the memory of G. M. Goluzin, and each paper has its own extensive bibliography. The author succeeds in capturing the interplay between the geometric properties of \(f(D)\) and the analytic properties of \(f\).
openaire   +2 more sources