Table of Contents

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


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© 2009
Academic Press
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“The text is simply unique. It doesn't compare to any other because its goals are different. It cannot be used as the only source of information for learning GMT, yet learning this subject without owning a copy of this book would be ridiculous since it gives a fast and efficient insight in many aspects of the theory.” -Thierry De Pauw, niversite catholique de Louvain, Belgium “The book is unique in its format and exposition. Without it, it would be difficult to get in touch with the subject. It paves the way to more advanced books. All other books on the market about this subject are rather technical and difficult to read for an inexperienced student.” -Stefan Wenger, Courant Institute of Math, New York University