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OverviewDie Theorie Riemannscher Flächen wird als ein Mikrokosmos der Reinen Mathematik dargestellt, in dem Methoden der Topologie und Geometrie, der komplexen und reellen Analysis sowie der Algebra zusammenwirken, um die reichhaltige Struktur dieser Flächen aufzuklären. Viele Beispiele und Bilder, die in der historischen Entwicklung eine Rolle spielten, ergänzen die Darstellung. Das Buch beruht auf Vorlesungen und Seminaren im Anschluß an eine Einführung in die komplexe Funktionentheorie. Wegen seiner Methodenvielfalt enthält es gleichzeitig Einführungen in die Topologie (Fundamentalgruppe, Überlagerungen, Flächen), in die algebraische Geometrie (Kurven und ihre Singularitäten) und in die Potentialtheorie (harmonische Funktionen). Die 2. Auflage wurde um eine genauere Betrachtung des Kleinschen 14-Ecks, ein Kapitel über die de Rhamsche Cohomologie und einen Paragraphen über die Lösung nicht-linearer Gleichungen der Mathematischen Physik mittels Riemannscher Thetafunktionen ergänzt. Full Product DetailsAuthor: Klaus LamotkePublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 2., erg. u. verb. Aufl. 2009 Dimensions: Width: 15.50cm , Height: 1.80cm , Length: 23.50cm Weight: 0.534kg ISBN: 9783642017100ISBN 10: 364201710 Pages: 341 Publication Date: 26 June 2009 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Language: German Table of ContentsGrundlagen.- Tori und elliptische Funktionen.- Fundamentalgruppen und #x00DC;berlagerungen.- Verzweigte #x00DC;berlagerungen.- Die - und #x03BB;-Funktion.- Algebraische Funktionen.- Differentialformen und Integration.- Divisoren und Abbildungen in projektive R#x00E4;ume.- Ebene Kurven.- Harmonische Funktionen.- Uniformisierung. Dreiecksgruppen.- Polyederfl#x00E4;chen.- Der Satz von Riemann-Roch.- Der Periodentorus.- Die deRhamsche Cohomologie.- Die Riemannsche Thetafunktion.ReviewsFrom the reviews of the second edition: The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered. (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009) From the reviews of the second edition: The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. ... This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered. (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009) From the reviews of the second edition: The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered. (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009) From the reviews of the second edition: The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered. (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009) From the reviews of the second edition: “The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. … This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered.” (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009) <p>From the reviews of the second edition: <p> The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered. (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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