Geometric Measure Theory

Geometric Measure Theory, Fourth Edition, is an excellent text for introducing ideas from geometric measure theory and the calculus of variations to beginning graduate students and researchers.

This updated edition contains abundant illustrations, examples, exercises, and solutions; and the latest results on soap bubble clusters, including a new chapter on Double Bubbles in Spheres, Gauss Space, and Tori. It also includes a new chapter on Manifolds with Density and Perelman's Proof of the Poincaré Conjecture.

This text is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject.

New to the 4th edition:

• Abundant illustrations, examples, exercises, and solutions.
• The latest results on soap bubble clusters, including a new chapter on "Double Bubbles in Spheres, Gauss Space, and Tori."
• A new chapter on "Manifolds with Density and Perelman's Proof of the Poincaré Conjecture."
• Contributions by undergraduates.

Advanced graduate students and researchers in mathematics.

Geometric Measure Theory Measures Lipschitz Functions and Rectifiable Sets Normal and Rectifiable Currents The Compactness Theorem and the Existence of Area-Minimizing Surfaces Examples 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 (M,E,)-Minimal Sets Miscellaneous Useful Results Soap Bubble Clusters Proof of Double Bubble Conjecture The Hexagonal Honeycomb and Kelvin Conjectures Immiscible Fluids and Crystals Isoperimetric Theorems in General Codimension Manifolds with Density and Perelman's Proof of the Poincaré Conjecture Double Bubbles in Spheres, Gauss Space, and Tori Solutions to Exercises