Differentialgeometrie und Minimalflächen (Springer-Lehrbuch by Jost-Hinrich Eschenburg,Jürgen Jost PDF

By Jost-Hinrich Eschenburg,Jürgen Jost

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 challenge. 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 einschließlich 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 pattern der modernen mathematischen Forschung. Verschiedene geistesgeschichtliche Bemerkungen runden den textual content ab. Die Neuauflage wurde überarbeitet und aktualisiert.

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Differentialgeometrie und Minimalflächen (Springer-Lehrbuch Masterclass) (German Edition) by Jost-Hinrich Eschenburg,Jürgen Jost


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