univalent function

A similar formula applies in the case of a pair of univalent functions (see below).

It plays an important role in the theory of univalent functions, conformal mapping and Teichmüller spaces.

The Koebe distortion theorem gives a series of bounds for a univalent function and its derivative.

The Grunsky inequalities imply many inequalities for univalent functions.

Univalent functions.

It is a remarkable fact, fundamental to the theory of univalent functions, that univalence is essentially preserved under uniform convergence.

The kernel theorem has wide application in the theory of univalent functions and in particular provides the geometric basis for the Loewner differential equation.

In 1968, the paper Open problems on univalent and multivalent functions, led to the two-volume set publication of Univalent Functions.

Inequalities for univalent functions on the unit disk can be proved by using the density for uniform convergence on compact subsets of slit mappings.

Frederick Gehring showed in 1977 that U is the interior of the closed subset of Schwarzian derivatives of univalent functions.

Zeev Nehari (born 2 February 1915 Berlin as Willi Weissbach; died 1978) was a mathematician who worked on univalent functions and on differential and integral equations.

The Loewner differential equation has led to inequalities for univalent functions that played an important role in the solution of the Bieberbach conjecture by Louis de Branges in 1985.

This was already known to imply the Robertson conjecture about odd univalent functions, which in turn was known to imply the Bieberbach conjecture about simple functions .

In mathematics, Nevalinna's criterion in complex analysis, proved in 1920 by the Finnish mathematician Rolf Nevanlinna, characterizes holomorphic univalent functions on the unit disk which are starlike.

In 1948, he wrote a mathematical conjecture on coefficients of -valent functions, as his dissertation thesis in Columbia University, followed by the paper Univalent functions and nonanalytic curves, published in 1957.

In mathematics, Grunsky's theorem, due to the German mathematician Helmut Grunsky, is a result in complex analysis concerning holomorphic univalent functions defined on the unit disk in the complex numbers.

The uniform convergence on compact sets of a sequence of holomorphic univalent functions, defined on the unit disk in the complex plane and fixing 0, can be formulated purely geometrically in terms of the limiting behaviour of the images of the functions.

He obtained his PhD in 1963 from the Courant Institute of Mathematical Sciences at New York University; his thesis was entitled A Boundary Value Problem Arising in the Theory of Univalent Functions and was supervised by Paul Garabedian.

Roughly speaking, the Grunsky inequalities give information on the coefficients of the logarithm of a univalent function; later generalizations by Milin, starting from the Lebedev-Milin inequality, succeeded in exponentiating the inequalities to obtain inequalities for the coefficients of the univalent function itself.