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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The Ahlfors Lectures Part I. One person found this helpful. Write a customer review. Amazon Quaziconformal Chance Pass it on, trade it in, give it a second life.
I probably wouldn’t recommend it as a first text, but for a serious student of the subject it’s worth reading eventually. Product details Format Paperback pages Dimensions This edition includes three new chapters.
Learn more about Amazon Giveaway. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics.
This edition includes three new chapters. It feels almost heresy to give this book anything less than a perfect, five star rating.
Lectures on Quasiconformal Mappings – Lars Valerian Ahlfors – Google Books
Conformal maps cannot do this, and a measure of how far the quasiconformal map is from being conformal involves the calculation of the dilatation quasicnformal a point. And following precedents from harmonic analysis, the author defines the Dirichlet integral, and shows it to be quasi-invariant under quasiconformal mappings.
The Teichmuller space is then shown to be an open subset of the space of quadratic differentials, with the Teichmuller metric giving the same metric as the norm in the space of quadratic differentials.
Ahlfors, of course, was one of the great mathematicians of the 20th century and made landmark contributions to several fields related to complex analysis, including the field of quasiconformal mappings. Second Edition Share this page.
Mori’s theorem is also proved, which gives a “Holder inequality”, i. A more general definition of a quasiconformal mapping is then given, that relaxes the Grotzsch requirement that the mappings be Quaslconformal.
Lectures on Quasiconformal Mappings: Second Edition
Table of Contents Lectures on Quasiconformal Mappings: Join our email list. Share your thoughts with other customers. The dilatation is computed by considering the effect that the linearization of a C1 homeomorphism has on circles.
Lars Ahlfors’ Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term ofwas first published in and was soon recognized as the classic it was shortly destined to become. The problem of finding the largest value jappings the module of this region is considered for three different conditions on this region and its bounded and unbounded components.
This short book gives a general overview of the important properties of quasiconformal mappings, with these goals and properties in mind.
Lectures on Quasiconformal Mappings: Second Edition
This then allows a homeomorphic extension to the closed mappinbs. Many graduate students and other mathematicians have learned the quaziconformal of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes.
The author then shows that K-quasiconformal mappings of the unit disk unto itself form a sequentially compact family with respect to uniform convergence. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings. Top Reviews Most recent Top Reviews. A topological mapping is called K-quasiconformal if the “modules” of quadrilaterals are K-quasi-invariant. For a family C of curves in the plane, the author introduces the extremal length of C, and shows that it is invariant under conformal mappings and “quasi-invariant” multiplied by a bounded factor under quasiconformal mappings.
The author introduces ahlrors study of quasiconformal mappings as natural generalizations of conformal mappings, as mappings less rigid than conformal lecturex, as mappings important in the study of elliptic partial differential equations, as generating interesting extremal problems, as important in moduli theory and Fuchsian and Kleinian groups, and as mappings that are better behaved in the context of several complex variables.
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