Geometric function theory is the study of geometric properties of analytic functions. A fundamental result in the theory is the Riemann mapping theorem...

function and its degree of approximation Geometric function theory, the study of geometric properties of analytic functions This disambiguation page lists mathematics...

traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers....

Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties...

In mathematics, geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli...

ISBN 0-07-000657-1 Ahlfors, Lars V. Conformal invariants. Topics in geometric function theory. Reprint of the 1973 original. With a foreword by Peter Duren...

ISBN 978-0226873756. Ahlfors, Lars V. (1973), Conformal invariants: topics in geometric function theory, New York: McGraw–Hill Book Co., MR 0357743 Constantin Carathéodory...

In mathematics, the geometric Langlands correspondence relates algebraic geometry and representation theory. It is a reformulation of the Langlands correspondence...

the seminorms being the suprema on compact subsets. From a geometric perspective, a function ⁠ f {\displaystyle f} ⁠ is holomorphic at ⁠ z 0 {\displaystyle...

mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R , {\displaystyle...

singularity of a complex-valued function of a complex variable. It is the simplest type of non-removable singularity of such a function (see essential singularity)...

points at which a multiple-valued function has nontrivial monodromy and an essential singularity. In geometric function theory, unqualified use of the term...

analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions...

Michigan, Kaczynski specialized in complex analysis, specifically geometric function theory. Professor Peter Duren said of Kaczynski, "He was an unusual person...

computational geometry. Geometric function theory the study of geometric properties of analytic functions. Geometric invariant theory a method for constructing...

punctured plane by the unit disc. This function is explicitly constructed in the theory of elliptic functions. If f {\textstyle f} omits two values, then...

Coefficient Bounds in the Theory of Univalent Functions and Nonoverlapping Domains", in Kuhnau, Reiner (ed.), Geometric Function Theory, Handbook of Complex...

In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: The probability distribution...

}{\frac {e^{itx}}{x^{2}+1}}\,dx} arises in probability theory when calculating the characteristic function of the Cauchy distribution. It resists the techniques...

de Toulouse. Série 2. 7 (3): 265–315. Titchmarsh, E. C. (1939). Theory of functions (2nd ed.). Oxford University Press. Hörmander, Lars (1966). An Introduction...

mathematics, a transformation, transform, or self-map is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X →...

G. (2001). Geometric function theory and non-linear analysis. Oxford. p. 32. Gray, J. D.; Morris, S. A. (April 1978). "When is a Function that Satisfies...

Goursat), is an important statement about line integrals for holomorphic functions in the complex plane. Essentially, it says that if f ( z ) {\displaystyle...

follows from the partial fraction form of the function, along with the formula for the sum of a geometric series, 1 z − a = − 1 a ∑ n = 0 ∞ ( z a ) n {\displaystyle...

terminology which also applied to arcs. In complex analysis and geometric function theory, quasicircles play a fundamental role in the description of the...

branches of complex geometry, and become an essential tool in the use of geometric PDE methods in complex geometry. Let D = { z : | z | < 1 } {\displaystyle...

poles of a meromorphic function to a contour integral of the function's logarithmic derivative. If f is a meromorphic function inside and on some closed...

Ernst Witt. Helmut Grunsky German, worked in complex analysis and geometric function theory. He introduced Grunsky's theorem and the Grunsky inequalities...

2007) was a Finnish mathematician, known for his research on geometric function theory. Heinonen, whose father was a lumberjack and local politician...

the 19th century in terms of set theory, and this greatly increased the possible applications of the concept. A function is often denoted by a letter such...