Geometric Measure Theory : Beginner's 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 and abundant illustrations and examples. This Second Edition features a new chapter on soap bubbles as well as updated sections addressing volume constraints, surfaces in manifolds, free boundaries, and Besicovitch constant results. The text will introduce newcomers to the field and appeal to mathematicians working in the field.
- Hardback | 250 pages
- 152 x 228 x 14mm | 498.96g
- 02 May 1995
- Elsevier Science Publishing Co Inc
- Academic Press Inc
- San Diego, United States
- 2nd Revised edition
- illustrations, bibliography, indexes
"This second edition continues to present an accessible and up-to-date source of the major advances in geometric measure theory. The book is intended to give the uninitiated a meaningful introduction to the subject by presenting basic ideas, terminology, and results in a framework that minimizes the plethora of associated technicalities and details. The author accomplishes this objective with resounding success. Moreover, the book also serves as a useful reference for those claiming some degree of expertise in this area since it provides an easily digested, macroscopic view of the subject as a result of its evolution during the past thirty-five years."--MATH REVIEWS
Table of contents
Geometric measure theory; measures; Lipschitz functions and rectifiable sets; normal and retifiable currents; the compactness theorem and the existence of area-minimizing surfaces; the approximation theorem; survey of regularity results; monotonicity and oriented tangent cones; the regularity of area-minimizing hypersurfaces; flat chains modulo v, varifolds and minimal sets; miscellaneous useful results; soap bubble clusters; solutions to exercises.