Geometric Measure Theory A Beginner's Guide

Geometric measure theory provides the framework to understand the structure of a crystal, a soap bubble cluster, or a universe. Over the past forty years it has contributed to major advances in geometry and analysis, including, for example, the original proof of the positive mass conjecture in cosmology. Undergraduates have made important contributions to the subject. This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the Double Bubble Conjecture (equal and unequal volumes) and the Hexagonal Honeycomb Conjecture. Within four new chapters, readers are also led through treatments of the Weaire-Phelan counterexample to the Kelvin conjecture, Almgren's optimal isoperimetric inequality, 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.Morgan, Frank is the author of 'Geometric Measure Theory A Beginner's Guide', published 2000 under ISBN 9780125068512 and ISBN 0125068514.