Geometric Measure Theory: A Beginner's Guide

Front Cover
Academic Press, 2016 M05 2 - 272 pages

Geometric Measure Theory: A Beginner's Guide, Fifth Edition provides the framework readers need to understand the structure of a crystal, a soap bubble cluster, or a universe.

The book is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Brevity, clarity, and scope make this classic book an excellent introduction to more complex ideas from geometric measure theory and the calculus of variations for beginning graduate students and researchers.

Morgan emphasizes geometry over proofs and technicalities, providing a fast and efficient insight into many aspects of the subject, with new coverage to this edition including topical coverage of the Log Convex Density Conjecture, a major new theorem at the center of an area of mathematics that has exploded since its appearance in Perelman's proof of the Poincaré conjecture, and new topical coverage of manifolds taking into account all recent research advances in theory and applications.

  • Focuses on core geometry rather than proofs, paving the way to fast and efficient insight into an extremely complex topic in geometric structures
  • Enables further study of more advanced topics and texts
  • Demonstrates in the simplest possible way how to relate concepts of geometric analysis by way of algebraic or topological techniques
  • Contains full topical coverage of The Log-Convex Density Conjecture
  • Comprehensively updated throughout
 

Selected pages

Contents

Applications
119
Solutions to Exercises
213
Bibliography
235
Index of Symbols
255
Name Index
257
Subject Index
259
On my way
264
Back Cover
265
Copyright

Other editions - View all

Geometric Measure Theory: A Beginner's Guide
Frank Morgan
No preview available - 2016

Common terms and phrases

2016 Frank Morgan Almgren approximately area-minimizing rectifiable current area-minimizing surface assume balls Borel boundary bounded codimension compactness theorem components constant convex Corollary countable curve define denote differential dimension disjoint Double Bubble Conjecture Elsevier Inc embedded manifold example exterior Figure finite flat chains follows Frank Morgan function f Gauss space Geometric Measure Theory Hausdorff dimension Hausdorff measure hence Hutchings hyperplanes hypersurface integral current integrand isoperimetric inequality least-area Lemma Lipschitz function m-vector manifolds with density mass mean curvature metric minimal surface minimal surface equation minimizing double bubble multiplicity normal current oriented tangent cone perimeter Poincaré Conjecture prescribed volumes proof Proposition proved Published by Elsevier rectifiable set regions regularity results Ricci curvature Riemannian manifold second variation singular set slices smooth soap bubble clusters soap film sphere standard double bubble submanifold symmetric Theorem Federer variation formula varifold yields

About the author (2016)

Frank Morgan is the Dennis Meenan '54 Third Century Professor of Mathematics at Williams College. He obtained his B.S. from MIT and his M.S. and Ph.D. from Princeton University. His research interest lies in minimal surfaces, studying the behavior and structure of minimizers in various settings. He has also written Riemannian Geometry: A Beginner's Guide, Calculus Lite, and most recently The Math Chat Book, based on his television program and column on the Mathematical Association of America Web site.

Bibliographic information

TitleGeometric Measure Theory: A Beginner's Guide
AuthorFrank Morgan
Edition5
PublisherAcademic Press, 2016
ISBN0128045272, 9780128045275
Length272 pages
  
Export CitationBiBTeX EndNote RefMan