Plateau's problem. An invitation to varifold geometry. (Q2758015)

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 [\textit{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 Many of the original hand-drawn figures by William Prokos have been replaced by figures produced using K. Brakke's Surface Evolver and J. Sullivan's rendering program.