Plateau’s Problem (Student Mathematical Library, V. 13) by Jr. Almgren, Frederick J. (PDF)

Description

This text is an invitation to the world of variational geometry. A central topic is Plateau’s Problem, which is concerned with surfaces that model the behaviour of soap films. When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This tool makes possible new analyses and new results.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is well-illustrated and motivates all of its theorems. In order to get anything out of this text, one should at least be familiar with basic algebraic topology of surfaces (I recommend Kinsey’s “Topology of Surfaces” for beginners) and should know the calculus of differential forms and chains in Spivak’s “Calculus on Manifolds”. It makes for a good read aftwerwards.

⭐

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