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Showing 1 to 7 of 7 for “"Geometric function theory"”.
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Some Inequalities Concerning Power Series and Their Interaction With Univalent Function Theory
Power series are fundamental in the study of Geometric Function Theory. In fact, they constitute a major part in Complex Analysis. The purpose of this dissertation is to employ analytic functions defined by power series in two different directions. The first of these discussed in Part I, mainly …
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Geometry of Ricci-flat Kähler manifolds and some counterexamples
… special Lagrangian fibrations using methods of geometric function theory. In particular, we generalize the method of extremal length and prove a generaliziation of the Teichmiiller theorem. We relate extremal problems to the existence of special Lagrangian fibrations in the large complex …
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The Asymptotic Behaviour of the Riemann Mapping Function at Analytic Cusps
… the upper half plane. One of the main topics in geometric function theory is to investigate the behaviour of the mapping functions at the boundary of such domains. In this work, we always assume that a piecewise analytic boundary is given. Hereby, we have to distinguish regular and singular …
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A New Approach to Lie Symmetry Groups of Minimal Surfaces
… of minimal surfaces by way of planar harmonic functions are determined. It is shown that a symmetry group acting on the minimal surfaces is isomorphic with H × H^2 — the analytic functions and the harmonic functions. A subgroup of this gives a generalization of the associated family which is …
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Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type
… geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. …
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The Lie Symmetries of a Few Classes of Harmonic Functions
… paper we will give a general background of the theory necessary to develop the ideas of working in the jet space of a given system of equations, applying this theory to harmonic functions in the complex plane. We will consider harmonic functions in general, harmonic functions with constant …