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Differentialgeometrie Und Minimalflächen by Jost-Hinrich Eschenburg, Jürgen Jost

Differentialgeometrie Und Minimalflächen

by Jost-Hinrich Eschenburg , Jürgen Jost
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Book cover type: Paperback
  • ISBN13: 9783642385216
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer Spektrum
  • Publisher Imprint: Springer Spektrum
  • Publication Date:
  • Pages: 258
  • Original Price: EUR 51.39
  • Language: German
  • Edition: 3., Aktualisier
  • Item Weight: 445 grams
  • BISAC Subject(s): Geometry / Differential

Das vorliegende Lehrbuch bietet eine moderne Einführung in die Differenzialgeometrie - etwa im Umfang einer einsemestrigen Vorlesung. Zunächst behandelt es die Geometrie von Flächen im Raum. Viele Beispiele schulen Leser in geometrischer Anschauung, deren wichtigste Klasse die Minimalflächen bilden. Zu ihrem Studium entwickeln die Autoren analytische Methoden und lösen in diesem Zusammenhang das Plateausche Problem. Es besteht darin, eine Minimalfläche mit vorgegebener Berandung zu finden. Als Beispiel einer globalen Aussage der Differenzialgeometrie beweisen sie den Bernsteinschen Satz. Weitere Kapitel behandeln die innere Geometrie von Flächen einschlie lich des Satzes von Gauss-Bonnet, und stellen die hyperbolische Geometrie ausführlich dar. Die Autoren verknüpfen geometrische Konstruktionen und analytische Methoden und folgen damit einem zentralen Trend der modernen mathematischen Forschung. Verschiedene geistesgeschichtliche Bemerkungen runden den Text ab. Die Neuauflage wurde überarbeitet und aktualisiert.
Hinweise und Errata auf Webseite des Autors: https: //myweb.rz.uni-augsburg.de/ eschenbu/

Prof. Dr. Jürgen Jost, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig
Prof. Dr. Jost-Hinrich Eschenburg, Universität Augsburg

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