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Author : Harvey Cohn
Publisher : Courier Corporation
Page : 352 pages
File Size : 42,6 Mb
Release : 2014-05-05
Category : Mathematics
ISBN : 9780486153292
Lucid, insightful exploration reviews complex analysis, introduces Riemann manifold, shows how to define real functions on manifolds, and more. Perfect for classroom use or independent study. 344 exercises. 1967 edition.
Author : Maurice Heins
Publisher : Unknown
Page : 16 pages
File Size : 51,9 Mb
Release : 1957
Category : Riemann surfaces
ISBN : UOM:39015095251453
Author : Lars Valerian Ahlfors,Leo Sario
Publisher : Princeton University Press
Page : 397 pages
File Size : 46,5 Mb
Release : 2015-12-08
Category : Mathematics
ISBN : 9781400874538
The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Samuil Leĭbovich Krushkalʹ
Publisher : Winston Publishing
Page : 344 pages
File Size : 40,8 Mb
Release : 1979
Category : Mathematics
ISBN : UCAL:B4980142
Author : Jürgen Jost
Publisher : Springer
Page : 143 pages
File Size : 51,6 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540388685
Author : Lars Valerian Ahlfors,E. Calabi,Marston Morse,Leo Sario,Donald Clayton Spencer
Publisher : Princeton University Press
Page : 264 pages
File Size : 44,6 Mb
Release : 1953-08-01
Category : Mathematics
ISBN : 9781400828371
The description for this book, Contributions to the Theory of Riemann Surfaces. (AM-30), Volume 30, will be forthcoming.
Author : Walter Helbig Gottschalk
Publisher : Unknown
Page : 176 pages
File Size : 42,7 Mb
Release : 1949
Category : Conformal mapping
ISBN : STANFORD:36105046454190
Author : R. Courant
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461299172
It has always been a temptation for mathematicians to present the crystallized product of their thoughts as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods of more general significance. The present book deals with subjects of this category. It is written in a style which, as the author hopes, expresses adequately the balance and tension between the individuality of mathematical objects and the generality of mathematical methods. The author has been interested in Dirichlet's Principle and its various applications since his days as a student under David Hilbert. Plans for writing a book on these topics were revived when Jesse Douglas' work suggested to him a close connection between Dirichlet's Principle and basic problems concerning minimal sur faces. But war work and other duties intervened; even now, after much delay, the book appears in a much less polished and complete form than the author would have liked."
Author : Leo Sario,Mitsuru Nakai
Publisher : Springer Science & Business Media
Page : 469 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642482694
The purpose of the present monograph is to systematically develop a classification theory of Riemann surfaces. Some first steps will also be taken toward a classification of Riemannian spaces. Four phases can be distinguished in the chronological background: the type problem; general classification; compactifications; and extension to higher dimensions. The type problem evolved in the following somewhat overlapping steps: the Riemann mapping theorem, the classical type problem, and the existence of Green's functions. The Riemann mapping theorem laid the foundation to classification theory: there are only two conformal equivalence classes of (noncompact) simply connected regions. Over half a century of efforts by leading mathematicians went into giving a rigorous proof of the theorem: RIEMANN, WEIERSTRASS, SCHWARZ, NEUMANN, POINCARE, HILBERT, WEYL, COURANT, OSGOOD, KOEBE, CARATHEODORY, MONTEL. The classical type problem was to determine whether a given simply connected covering surface of the plane is conformally equivalent to the plane or the disko The problem was in the center of interest in the thirties and early forties, with AHLFORS, KAKUTANI, KOBAYASHI, P. MYRBERG, NEVANLINNA, SPEISER, TEICHMÜLLER and others obtaining incisive specific results. The main problem of finding necessary and sufficient conditions remains, however, unsolved.
Author : Anonim
Publisher : Bookboon
Page : 115 pages
File Size : 45,5 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9788776817022
Author : Dr. Jörg Richter
Publisher : Unknown
Page : 97 pages
File Size : 42,5 Mb
Release : 1997-09-01
Category : Mathematics
ISBN : 8210379456XXX
In the present work, a coordinate-free way is suggested to handle conformal maps of a Riemannian surface into a space of constant curvature of maximum dimension 4, modeled on the non-commutative field of quaternions. This setup for the target space and the idea to treat differential 2-forms on Riemannian surfaces as quadratic functions on the tangent space, are the starting points for the development of the theory of conformal maps and in particular of conformal immersions. As a first result, very nice conditions for the conformality of immersions into 3- and 4-dimensional space-forms are deduced and a simple way to write the second fundamental form is found. If the target space is euclidean 3-space, an alternative approach is proposed by fixing a spin structure on the Riemannian surface. The problem of finding a local immersion is then reduced to that of solving a linear Dirac equation with a potential whose square is the Willmore integrand. This allows to make statements about the structure of the moduli space of conformal immersions and to derive a very nice criterion for a conformal immersion to be constrained Willmore. As an application the Dirac equation with constant potential over spheres and tori is solved. This yields explicit immersion formulae out of which there were produced pictures, the Dirac-spheres and -tori. These immersions have the property that their Willmore integrand generates a metric of vanishing and constant curvature, respectively. As a next step an affine immersion theory is developped. This means, one starts with a given conformal immersion into euclidean 3-space and looks for new ones in the same conformal class. This is called a spin-transformation and it leads one to solve an affine Dirac equation. Also, it is shown how the coordinate-dependent generalized Weierstrass representation fits into the present framework. In particular, it is now natural to consider the class of conformal immersions that admit new conformal immersions having the same potential. It turns out, that all geometrically interesting immersions admit such an isopotential spin-transformation and that this property of an immersion is even a conformal invariant of the ambient space. It is shown that conformal isothermal immersions generate both via their dual and via Darboux transformations non-trivial families of new isopotential conformal immersions. Similarly to this, conformal (constrained) Willmore immersions produce non-trivial families of isopotential immersions of which subfamilies are (constrained) Willmore again having even the same Willmore integral. Another observation is, that the Euler-Lagrange equation for the Willmore problem is the integrability condition for a quaternionic 1-form, which generates a conformal minimal immersions into hyperbolic 4-space. Vice versa, any such immersion determines a conformal Willmore immersion. As a consequence, there is a one-to-one correspondence between conformal minimal immersions into Lorentzian space and those into hyperbolic space, which generalizes to any dimension. There is also induced an action on conformal minimal immersions into hyperbolic 4-space. Another fact is, that conformal constant mean curvature (cmc) immersions into some 3-dimensional space form unveil to be isothermal and constrained Willmore. The reverse statement is true at least for tori. Finally a very simple proof of a theorem by R.Bryant concerning Willmore spheres is given. In the last part, time-dependent conformal immersions are considered. Their deformation formulae are computed and it is investigated under what conditions the flow commutes with Moebius transformations. The modified Novikov-Veselov flow is written down in a conformal invariant way and explicit deformation formulae for the immersion function itself and all of its invariants are given. This flow commutes with Moebius transformations. Its definition is coupled with a delta-bar problem, for which a solution is presented under special conditions. These are fulfilled at least by cmc immersions and by surfaces of revolution and the general flow formulae reduce to very nice formulae in these cases.
Author : Tapani Jussila
Publisher : Unknown
Page : 48 pages
File Size : 45,8 Mb
Release : 1988
Category : Riemann surfaces
ISBN : UCSD:31822003012879
Author : Lars Valerian Ahlfors,Leo Sario
Publisher : Unknown
Page : 0 pages
File Size : 48,5 Mb
Release : 2015
Category : MATHEMATICS
ISBN : OCLC:1248694877
The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions.Originally published in 1960.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 45,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662034460
This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.
Author : George Springer
Publisher : Chelsea Publishing Company, Incorporated
Page : 326 pages
File Size : 50,9 Mb
Release : 1981
Category : Mathematics
ISBN : UOM:39015015698288
This text aims to introduce the reader to Riemann surfaces.