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Geometric Measure Theory and the Calculus of Variations

Allard, William K.

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ISBN 10: 0821814702 / ISBN 13: 9780821814703
Published by Amer Mathematical Society, 1986
Used Condition: Fine
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0821814702 0821814702 Fine. (Binding: Hardcover, Jacket: No Jacket) Hardcover, fine condition, no jacket. Bookseller Inventory # 1076222

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Bibliographic Details

Title: Geometric Measure Theory and the Calculus of...

Publisher: Amer Mathematical Society

Publication Date: 1986

Book Condition:Fine

About this title


These twenty-six papers survey a cross section of current work in modern geometric measure theory and its applications in the calculus of variations. Presently the field consists of a jumble of new ideas, techniques and intuitive hunches; an exchange of information has been hindered, however, by the characteristic length and complexity of formal research papers in higher-dimensional geometric analysis. This volume provides an easier access to the material, including introductions and summaries of many of the authors' much longer works and a section containing 80 open problems in the field.The papers are aimed at analysts and geometers who may use geometric measure-theoretic techniques, and they require a mathematical sophistication at the level of a second year graduate student. The papers included were presented at the 1984 AMS Summer Research Institute held at Humboldt State University. A major theme of this institute was the introduction and application of multiple-valued function techniques as a basic new tool in geometric analysis, highlighted by Almgren's fundamental paper Deformations and multiple-valued functions. Major new results discussed at the conference included the following: Allard's integrality and regularity theorems for surfaces stationary with respect to general elliptic integrands; Scheffer's first example of a singular solution to the Navier-Stokes equations for a fluid flow with opposing force; and, Hutchinson's new definition of the second fundamental form of a general varifold.

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