Lars Ahlfors’ Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of , was first published in and. Lectures on Quasiconformal Mappings. Front Cover. Lars Valerian Ahlfors. Van Nostrand, – Conformal mapping – pages. Lectures on quasiconformal mappings / by Lars V. Ahlfors ; manuscript prepared with the assistance of Clifford J. Earle, Jr Ahlfors, Lars Valerian,
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Join our email list. Get to Know Us. We use cookies to give you the best possible experience. Acknowledgments Differentiable quasiconformal mappings The general definition Extremal geometric properties Boundary correspondence The mapping theorem Teichmuller spaces Editors’ notes The Additional Chapters: Amazon Music Stream millions of songs.
Some details, such as the definition of module conformal modulus at the start of Chapter 3, seem missing altogether. A supplement to Ahlfors’s lectures Complex dynamics and quasiconformal mappings Hyperbolic structures on three-manifolds that fiber over the circle.
As the author notes, quasiconformal mappings were introduced by the mathematician H. Showing of 2 reviews. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. This short book gives a general overview of the important properties of quasiconformal mappings, with these goals and properties in mind.
The Teichmuller space is thus defined as the collection of pairs of Riemann surfaces and sense-preserving quasiconformal mappings between them, with pairs being equivalent under homotopy.
Lectures on Quasiconformal Mappings : Lars V Ahlfors :
Volume I Grundlehren der mathematischen Wissenschaften. He then studies the extent to which quasiconformal mappings are isometries, called “quasi-isometries” where distances are multiplied by a bounded factor.
See our librarian page for additional eBook ordering options. Libraries and resellers, please contact cust-serv ams. Amazon Advertising Find, attract, and engage customers. Ahlfors, of course, was one of the great mathematicians of the 20th ahlforw and made landmark contributions to several fields related to complex analysis, including the field of quasiconformal mappings.
It feels almost heresy to give this book anything quasiconformaal than a perfect, five star rating. It is nevertheless a useful and enjoyable book, in that you get a firsthand glimpse into the theory while still mid-development, you get the same content as some of Ahlfors’s papers while packaged into a more self-contained exposition, and you find some “hard analysis” arguments for example, using elliptic functions that seem to be deemphasized in more recent books.
The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings.
I probably wouldn’t recommend it as a first text, but for a serious student of the subject it’s worth reading eventually. This edition includes three new chapters. Other books in this series.
Lectures on Quasiconformal Mappings: Second Edition
He then considers the question as to when quadruples of distinct complex numbers can be mapped to each other under K-quasiconformal mappings. Would you like to tell us about a lower price? One person found this helpful. Write a customer review. Lectures on Chevalley Groups Robert Steinberg. Second Edition Share this page. Qkasiconformal 1 of 1 Start over Page 1 of 1. Alexa Actionable Analytics for the Web. Grotzsch in as mappings that are as close to conformal as possible, but that can, for example, take a square in the plane and map it to a non-square rectangle in the plane, mapping vertices onto vertices in the process.
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Print Price 2 Label: A topological mapping is called K-quasiconformal if the “modules” of quadrilaterals are K-quasi-invariant. By using our website you agree to our use quasicoformal cookies.
The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. There’s a problem loading this menu right now.
This space has dimension 3g – 3 when the starting Riemann surface has genus g, and with respect to the parameters of the basis of this space, one obtains a holomorphic family of Riemann surfaces.
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Lectures on Quasiconformal Mappings – Lars Valerian Ahlfors – Google Books
Amazon Giveaway mapping you to run promotional lectires in order to create buzz, reward your audience, and attract new followers and customers. The dilatation is computed by considering the effect that the linearization of a C1 homeomorphism has on circles.
Withoutabox Submit to Film Festivals. The third, by Hubbard, illustrates the role of these mappings in Thurston’s theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings. Set up a giveaway.