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Zbl 0995.49001
Almgren, Frederick J.jun.
Plateau's problem. An invitation to varifold geometry. Revised ed. (English)
[B] Student Mathematical Library. 13. Providence, RI: American Mathematical Society (AMS). xvi, 78 p. \$ 19.00 (2001). ISBN 0-8218-2747-2/pbk

This book is a republication of the late author's 1966 monograph [originally published by W. A. Benjamin, Inc. (1966; Zbl 0165.13201)]. Because the author's original paper ``The theory of varifolds -- A variational calculus in the large for the $k$-dimensional area integrand'' was never published, the original monograph provided the first appearance of the notion of a varifold in a widely available form. Subsequently, the definition of a varifold was recast in [{\it W. K. Allard}, Ann. Math., II. Ser. 95, 417-491 (1972; Zbl 0252.49028)]; this recasting of the definition is noted in the forward and in a footnote to the definition. Additions to this edition are a foreword by J. Taylor and a section of additional references. Many of the original hand-drawn figures by William Prokos have been replaced by figures produced using K. Brakke's Surface Evolver and J. Sullivan's rendering program.
[H.Parks (Corvallis)]

MSC 2000:: *49-01 Textbooks (calculus of variations)
49Q15 Geometric measure and integration theory, etc.
49Q20 Variational problems in geometric measure-theoretic setting
28A75 Geometric measure theory
58E12 Appl. of variational methods to minimal surfaces

Keywords: least area problem; integration of differential forms; varifolds; rectifiable geometry; variational problems

Citations: Zbl 0165.13201; Zbl 0252.49028

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