HOtrary Riemann surfaces in a given homotopy class of homeomorphisms. This result is a wide generalization of a result of Gr otzsch on mappings between rectangles. Teichmuller proved this theorem in the two papers. Motivated by his work on extremal quasiconformal mappings. He wrote a paper. QUASICONFORMAL MAPPINGS AND SCHWARZ& 39; S LEMMAIn this paper. **Quasiconformal Surfaces and Riemann Surfaces - Samuil L. Krushkal**

K quasiconformal maps of Riemann surfaces are investi- gated. Which is similar to Schwarz& 39; s lemma. Is proved for a certain class of K quasiconformal maps. This result is then used to give elementary proofs of theorems concerning K quasiconformal maps. These include Schottky& 39; s lemma. Liouville& 39; s theorem. And the big Picard theorem. Some of Huber& 39; s results on analytic. **Quasiconformal Surfaces and Riemann Surfaces - Samuil L. Krushkal**

Moduli of Riemann surfaces. “ Complex- analytic structure in the space of closed Riemann surfaces, ” in. Spaces of Riemann Surfaces and Quasiconformal Mappings. Russian translation. Computing Quasiconformal Maps on Riemann surfaces using. Computing Quasiconformal Maps on Riemann surfaces using Discrete Curvature Flow. Surface mapping plays an important role in geometric processing. **Quasiconformal Surfaces and Riemann Surfaces - Samuil L. Krushkal**

They induce both area and angular distortions. If the angular distortion is bounded. On quasiconformal mappings of open Riemann surfaces. Discontinuous Groups and Riemann surfaces. MathSciNet Google Scholar. On the geometry of the metric induced by a quadratic differential I and II. Bulletin de la société des sciences et des lettres de Łódź. **Quasiconformal Surfaces and Riemann Surfaces - Samuil L. Krushkal**

On quasiconformal mappings of open Riemann surfaces - PDF. On quasiconformal mappings of open Riemann surfaces 305 T h e r e f o r e the set of all points P c 3 with la + P I. A is relatively open. And the set E~ =. Intersection of d e n u m e r a b l y m a n y relatively o p e n sets. Let PocE= and assume that a ~ with initial point. Lecture notes for the course V5D3 - Advanced Topics in. Riemann surfaces 9 1. **Quasiconformal Surfaces and Riemann Surfaces - Samuil L. Krushkal**

Hyperbolic surfaces 12 1. Exercises 13 Lecture 2. Tori and spheres 15 2. Quotients revisited 15 2. The uniformization theorem and automorphism groups 16 2. Quotients of the three simply connected Riemann surfaces 17 2. Exercises 20 Lecture 3. **Quasiconformal Surfaces and Riemann Surfaces - Samuil L. Krushkal**

More on quotients and conformal structures 21 3. Quotients of the upper half plane. SQUARE INTEGRABLE DIFFERENTIALS ON RIEMANN SURFACES AND. RIEMANN SURFACES AND QUASICONFORMAL MAPPINGS BY CARL DAVID MINDA ABSTRACT. R — * R is a quasiconformal homeomorphism of Riemann surfaces. Then Marden showed that. Naturally induces an isomorphism of the corresponding Hilbert spaces of square integrable first- order differential forms. **Quasiconformal Surfaces and Riemann Surfaces - Samuil L. Krushkal**

It is demonstrated that this isomorphism preserves many important subspaces. Preliminary to this. Square Integrable Differentials on Riemann Surfaces. R→ R& 39; is a quasiconformal homeomorphism of Riemann surfaces. Then Marden showed that naturally induces an isomorphism of the corresponding Hilbert spaces of square integrable first- order. Alexander Bobenko - TU BerlinRiemann surfaces can be described in many completely di erent ways. Interrelations between these descriptions comprise an essential part of the theory. **Quasiconformal Surfaces and Riemann Surfaces - Samuil L. Krushkal**

The basic examples of Riemann surfaces we are going to discuss now are exactly these foundation stones the whole theory is based on. 1 Non- singular Algebraic Curves De nition 1. 2 An algebraic curve Cis a subset in C2 C= f. **Quasiconformal Surfaces and Riemann Surfaces - Samuil L. Krushkal**

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