Harmonic Mappings in the Plane

Harmonic Mappings in the Plane

Author: Peter Duren

Publisher: Cambridge University Press

Published: 2004-03-29

Total Pages: 236

ISBN-13: 9781139451277

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Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry.


Book Synopsis Harmonic Mappings in the Plane by : Peter Duren

Download or read book Harmonic Mappings in the Plane written by Peter Duren and published by Cambridge University Press. This book was released on 2004-03-29 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry.

Quasiconformal Mappings in the Plane

Quasiconformal Mappings in the Plane

Author: J. Krzyz

Publisher: Springer

Published: 2006-11-15

Total Pages: 185

ISBN-13: 3540394648

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Book Synopsis Quasiconformal Mappings in the Plane by : J. Krzyz

Download or read book Quasiconformal Mappings in the Plane written by J. Krzyz and published by Springer. This book was released on 2006-11-15 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)

Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)

Author: Kari Astala

Publisher: Princeton University Press

Published: 2009-01-18

Total Pages: 708

ISBN-13: 9780691137773

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This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.


Book Synopsis Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48) by : Kari Astala

Download or read book Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48) written by Kari Astala and published by Princeton University Press. This book was released on 2009-01-18 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.

Geometry of the Plane Cremona Maps

Geometry of the Plane Cremona Maps

Author: Maria Alberich-Carraminana

Publisher: Springer

Published: 2004-10-20

Total Pages: 262

ISBN-13: 3540455388

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This book provides a self-contained exposition of the theory of plane Cremona maps, reviewing the classical theory. The book updates, correctly proves and generalises a number of classical results by allowing any configuration of singularities for the base points of the plane Cremona maps. It also presents some material which has only appeared in research papers and includes new, previously unpublished results. This book will be useful as a reference text for any researcher who is interested in the topic of plane birational maps.


Book Synopsis Geometry of the Plane Cremona Maps by : Maria Alberich-Carraminana

Download or read book Geometry of the Plane Cremona Maps written by Maria Alberich-Carraminana and published by Springer. This book was released on 2004-10-20 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained exposition of the theory of plane Cremona maps, reviewing the classical theory. The book updates, correctly proves and generalises a number of classical results by allowing any configuration of singularities for the base points of the plane Cremona maps. It also presents some material which has only appeared in research papers and includes new, previously unpublished results. This book will be useful as a reference text for any researcher who is interested in the topic of plane birational maps.

Quasiconformal Mappings in the Plane

Quasiconformal Mappings in the Plane

Author: Olli Lehto

Publisher:

Published: 1973

Total Pages: 274

ISBN-13:

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Book Synopsis Quasiconformal Mappings in the Plane by : Olli Lehto

Download or read book Quasiconformal Mappings in the Plane written by Olli Lehto and published by . This book was released on 1973 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quasiconformal Mappings in the Plane

Quasiconformal Mappings in the Plane

Author: Olli Lehto

Publisher: Springer

Published: 1973

Total Pages: 0

ISBN-13: 9783642655135

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Book Synopsis Quasiconformal Mappings in the Plane by : Olli Lehto

Download or read book Quasiconformal Mappings in the Plane written by Olli Lehto and published by Springer. This book was released on 1973 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mappings of the Plane

Mappings of the Plane

Author: Gwen Harwood

Publisher: Carcanet

Published: 2009-05-28

Total Pages: 165

ISBN-13: 1847778992

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Gwen Harwood (1920-1995) is one of the best loved Australian poets of the twentieth century - and a fierce prankster, who published poems under half-a-dozen names and identities. By turns poignant, sensuous and mischievous, passionately musical, her poetry is marked by sure intelligence and a quicksilver, anti-authoritarian wit. This new selection of her poetry from 1943 to her death makes the full range of the work accessible for the first time to poetry-lovers in the northern hemisphere. With an introduction by the leading Harwood critic Gregory Kratzmann and the Australian poet Chris Wallace-Crabbe, who corresponded with Harwood, the selection includes hitherto little-known work along with poems which have become part of the central canon of Australian poetry.


Book Synopsis Mappings of the Plane by : Gwen Harwood

Download or read book Mappings of the Plane written by Gwen Harwood and published by Carcanet. This book was released on 2009-05-28 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gwen Harwood (1920-1995) is one of the best loved Australian poets of the twentieth century - and a fierce prankster, who published poems under half-a-dozen names and identities. By turns poignant, sensuous and mischievous, passionately musical, her poetry is marked by sure intelligence and a quicksilver, anti-authoritarian wit. This new selection of her poetry from 1943 to her death makes the full range of the work accessible for the first time to poetry-lovers in the northern hemisphere. With an introduction by the leading Harwood critic Gregory Kratzmann and the Australian poet Chris Wallace-Crabbe, who corresponded with Harwood, the selection includes hitherto little-known work along with poems which have become part of the central canon of Australian poetry.

Airline Maps

Airline Maps

Author: Mark Ovenden

Publisher: Penguin

Published: 2019-10-29

Total Pages: 146

ISBN-13: 0143134078

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A nostalgic and celebratory look back at one hundred years of passenger flight, featuring full-color reproductions of route maps and posters from the world's most iconic airlines, from the author of bestselling cult classic Transit Maps of the World. In this gorgeously illustrated collection of airline route maps, Mark Ovenden and Maxwell Roberts look to the skies and transport readers to another time. Hundreds of images span a century of passenger flight, from the rudimentary trajectory of routes to the most intricately detailed birds-eye views of the land to be flown over. Advertisements for the first scheduled commercial passenger flights featured only a few destinations, with stunning views of the countryside and graphics of biplanes. As aviation took off, speed and mileage were trumpeted on bold posters featuring busy routes. Major airlines produced highly stylized illustrations of their global presence, establishing now-classic brands. With trendy and forward-looking designs, cartographers celebrated the coming together of different cultures and made the earth look ever smaller. Eventually, fleets got bigger and routes multiplied, and graphic designers have found creative new ways to display huge amounts of information. Airline hubs bring their own cultural mark and advertise their plentiful destination options. Innovative maps depict our busy world with webs of overlapping routes and networks of low-cost city-to-city hopping. But though flying has become more commonplace, Ovenden and Roberts remind us that early air travel was a glamorous affair for good reason. Airline Maps is a celebration of graphic design, cartographic skills and clever marketing, and a visual feast that reminds us to enjoy the journey as much as the destination.


Book Synopsis Airline Maps by : Mark Ovenden

Download or read book Airline Maps written by Mark Ovenden and published by Penguin. This book was released on 2019-10-29 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: A nostalgic and celebratory look back at one hundred years of passenger flight, featuring full-color reproductions of route maps and posters from the world's most iconic airlines, from the author of bestselling cult classic Transit Maps of the World. In this gorgeously illustrated collection of airline route maps, Mark Ovenden and Maxwell Roberts look to the skies and transport readers to another time. Hundreds of images span a century of passenger flight, from the rudimentary trajectory of routes to the most intricately detailed birds-eye views of the land to be flown over. Advertisements for the first scheduled commercial passenger flights featured only a few destinations, with stunning views of the countryside and graphics of biplanes. As aviation took off, speed and mileage were trumpeted on bold posters featuring busy routes. Major airlines produced highly stylized illustrations of their global presence, establishing now-classic brands. With trendy and forward-looking designs, cartographers celebrated the coming together of different cultures and made the earth look ever smaller. Eventually, fleets got bigger and routes multiplied, and graphic designers have found creative new ways to display huge amounts of information. Airline hubs bring their own cultural mark and advertise their plentiful destination options. Innovative maps depict our busy world with webs of overlapping routes and networks of low-cost city-to-city hopping. But though flying has become more commonplace, Ovenden and Roberts remind us that early air travel was a glamorous affair for good reason. Airline Maps is a celebration of graphic design, cartographic skills and clever marketing, and a visual feast that reminds us to enjoy the journey as much as the destination.

Mappings of the Plane

Mappings of the Plane

Author: H. E. Chrestenson

Publisher:

Published: 1966

Total Pages: 188

ISBN-13:

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Book Synopsis Mappings of the Plane by : H. E. Chrestenson

Download or read book Mappings of the Plane written by H. E. Chrestenson and published by . This book was released on 1966 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Reciprocity, Spatial Mapping and Time Reversal in Electromagnetics

Reciprocity, Spatial Mapping and Time Reversal in Electromagnetics

Author: C. Altman

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 299

ISBN-13: 9401579156

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The choice of topics in this book may seem somewhat arbitrary, even though we have attempted to organize them in a logical structure. The contents reflect the path of 'search and discovery' followed by us, on and off, for the in fact last twenty years. In the winter of 1970-71 one of the authors (C. A. ), on sah baticalleave with L. R. O. Storey's research team at the Groupe de Recherches Ionospheriques at Saint-Maur in France, had been finding almost exact symme tries in the computed reflection and transmission matrices for plane-stratified magnetoplasmas when symmetrically related directions of incidence were com pared. At the suggestion of the other author (K. S. , also on leave at the same institute), the complex conjugate wave fields, used to construct the eigenmode amplitudes via the mean Poynting flux densities, were replaced by the adjoint wave fields that would propagate in a medium with transposed constitutve tensors, et voila, a scattering theorem-'reciprocity in k-space'-was found in the computer output. To prove the result analytically one had to investigate the properties of the adjoint Maxwell system, and the two independent proofs that followed, in 1975 and 1979, proceeded respectively via the matrizant method and the thin-layer scattering-matrix method for solving the scattering problem, according to the personal preferences of each of the authors. The proof given in Chap. 2 of this book, based on the hindsight provided by our later results, is simpler and much more concise.


Book Synopsis Reciprocity, Spatial Mapping and Time Reversal in Electromagnetics by : C. Altman

Download or read book Reciprocity, Spatial Mapping and Time Reversal in Electromagnetics written by C. Altman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: The choice of topics in this book may seem somewhat arbitrary, even though we have attempted to organize them in a logical structure. The contents reflect the path of 'search and discovery' followed by us, on and off, for the in fact last twenty years. In the winter of 1970-71 one of the authors (C. A. ), on sah baticalleave with L. R. O. Storey's research team at the Groupe de Recherches Ionospheriques at Saint-Maur in France, had been finding almost exact symme tries in the computed reflection and transmission matrices for plane-stratified magnetoplasmas when symmetrically related directions of incidence were com pared. At the suggestion of the other author (K. S. , also on leave at the same institute), the complex conjugate wave fields, used to construct the eigenmode amplitudes via the mean Poynting flux densities, were replaced by the adjoint wave fields that would propagate in a medium with transposed constitutve tensors, et voila, a scattering theorem-'reciprocity in k-space'-was found in the computer output. To prove the result analytically one had to investigate the properties of the adjoint Maxwell system, and the two independent proofs that followed, in 1975 and 1979, proceeded respectively via the matrizant method and the thin-layer scattering-matrix method for solving the scattering problem, according to the personal preferences of each of the authors. The proof given in Chap. 2 of this book, based on the hindsight provided by our later results, is simpler and much more concise.