Geometric Measure Theory: A Beginners Guide

Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Morgan emphasizes geometry over proofs and technicalities, and includes a bibliography. This Second Edition features a new chapter on soap bubbles.

Geometric measure theory is the mathematical framework for the study of crystal growth, the geometry of clusters of soap bubbles, and similar structures involving minimization of surface energy. Beautiful mathematics comes into play when a group of bubbles forms a cluster and physically solves the complicated mathematical problem of minimizing surface energy.

This Second Edition, intended for newcomers to the field of geometric measure theory, emphasizes geometry over proofs and technicalities, and includes a bibliography, abundant illustrations, exercises, and examples. Old hands will enjoy it as well, especially its new features: a new chapter on soap bubbles, as well as updated sections addressing volume contraints, surfaces in manifolds, free boundaries, general integrands, calibrations, and the recent disproof of Kelvin's Conjecture. The text will introduce newcomers to the field and appeal to those working in the field.

Frank Morgan works in minimal surfaces and studies the behavior and structure of minimizers in various settings. He is also the author of Riemannian Geometry: A Beginners Guide and Calculus Life.