Geometric Measure Theory: A Beginner's Guide

von Frank Morgan Kategorie: Mengenlehre ISBN: 0125068514 Kommentar abgeben

Kurzbeschreibung Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. It has contributed over the past thirty years to major advances in geometry and analysis, including, for example, the original proof of the positive mass conjecture in cosmology. The subject is receiving more and more attention. 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 and the Hexagonal Honeycomb Conjecture. Within four new chapters, readers are also led through treatments of the Weaire-Phelan counterexample to 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.

Synopsis Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. It has contributed to major advances in geometry and analysis, including, for example, the original proof of the positive mass conjecture in cosmology. This third edition of "Geometric Measure Theory: A Beginner's Guide" presents the proofs of the Double Bubble Conjecture and the Hexagonal Honeycomb Conjecture. Within four new...