Geometric Measure Theory: A Beginner's Guide, 3 Ed

Frank Morgan, "Geometric Measure Theory: A Beginner's Guide, 3 Ed"
Academic Press | 2000 | ISBN: 0125068514 | 221 pages | File type: PDF | 16,3 mb

Geometric measure theory could be described as differential geometry, generalized through measure theory to deal with maps and surfaces that are not necessarily smooth, and applied to the calculus of variations. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Over the past thirty years, this theory has contributed to major advances in geometry and analysis including, for example, the original proof of the positive mass conjecture in cosmology.

Four new chapters lead the reader through treatments of the Weaire-Phelan counter example of Kelvin's conjecture, Almgren's optimal isoperimetric inequality, and immiscible fluids and crystals. The abundant illustrations, examples, exercises, and solutions in this book will enhance its reputation as the most accessible introduction to the subject.


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