Geometric Measure Theory

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.

Geometric Measure TheoryMeasuresLipschitz Functions and Rectifiable SetsNormal and Rectifiable CurrentsThe Compactness Theorem and the Existence of Area-Minimizing SurfacesExamples of Area-Minimizing SurfacesThe Approximation Theorem Survey of Regularity ResultsMonotonicity and Oriented Tangent ConesThe Regularity of Area-Minimizing HypersurfacesFlat Chains Modulo v, Varifolds, and (M,E,)-Minimal SetsMiscellaneous Useful ResultsSoap Bubble ClustersProof of Double Bubble ConjectureThe Hexagonal Honeycomb and Kelvin ConjecturesImmiscible Fluids and CrystalsIsoperimetric Theorems in General CodimensionManifolds with Density and Perelman's Proof of the Poincaré ConjectureDouble Bubbles in Spheres, Gauss Space, and ToriSolutions to Exercises