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Plateau’s problem. An invitation to varifold geometry. Revised ed. (English) Zbl 0995.49001
Student Mathematical Library. 13. Providence, RI: American Mathematical Society (AMS). xvi, 78 p. $ 19.00 (2001).
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 [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 Many of the original hand-drawn figures by William Prokos have been replaced by figures produced using K. Brakke’s Surface Evolver and J. Sullivan’s rendering program.
MSC:
49-01Textbooks (calculus of variations)
49Q15Geometric measure and integration theory, integral and normal currents (optimization)
49Q20Variational problems in a geometric measure-theoretic setting
28A75Length, area, volume, other geometric measure theory
58E12Applications of variational methods to minimal surfaces