Global Theory of Minimal Surfaces: Proceedings of the Clay Mathematics Institute 2001 Summer School, Mathematics Sciences Research Institute, Berkeley, California June 25-July 27, 200(Clay Mathematics Proceedings)

In the Summer of 2001, the Mathematical Sciences Research Institute (MSRI) hosted the Clay Mathematics Institute Summer School on the Global Theory of Minimal Surfaces. During that time, MSRI became the world center for the study of minimal surfaces: 150 mathematicians - undergraduates, post-doctoral students, young researchers, and world experts - participated in the most extensive meeting ever held on the subject in its 250-year history.The unusual nature of the meeting made it possible to put together this collection of expository lectures and specialized reports, giving a panoramic view of a vital subject presented by leading researchers in the field. The subjects covered include minimal and constant-mean-curvature submanifolds, geometric measure theory and the double-bubble conjecture, Lagrangian geometry, numerical simulation of geometric phenomena, applications of mean curvature to general relativity and Riemannian geometry, the isoperimetric problem, the geometry of fully nonlinear elliptic equations and applications to the topology of three-dimensional manifolds. The wide variety of topics covered make this volume suitable for graduate students and researchers interested in differential geometry.

Table of Contents:
Geometric measure theory and the proof of the double bubble conjecture by F. Morgan and M. Ritore Classical minimal surfaces in Euclidean space by examples: Geometric and computational aspects of the Weierstrass representation by M. Weber Computational aspects of discrete minimal surfaces by K. Polthier Mean curvature in Riemannian geometry and general relativity by R. Schoen Introduction to conjugate Plateau constructions by H. Karcher Parabolicity and minimal surfaces by J. Perez and F. J. Lopez The isoperimetric problem by A. Ros Flat structures, Teichmuller theory and handle addition for minimal surfaces by M. Wolf The genus-one helicoid as a limit of screw-motion invariant helicoids with handles by M. Weber, D. Hoffman, and M. Wolf Computing minimal surfaces by D. Hoffman Geometric aspects of the theory of fully nonlinear elliptic equations by J. Spruck Hyperbolic surfaces of constant mean curvature one with compact fundamental domains by H. Karcher Isoperimetric inequalities of minimal submanifolds by J. Choe Complete nonorientable minimal surfaces in $\mathbb{R}^3$ by F. Martin Some Picard-type results for properly immersed minimal surfaces in $\mathbb{R}^3$ by F. J. Lopez Optimal isoperimetric inequalities for three-dimensional Cartan-Hadamard manifolds by M. Ritore Embedded minimal disks by T. H. Colding and W. P. Minicozzi II Construction of minimal surfaces by gluing Weierstrass representations by M. Traizet Global problems in classical minimal surface theory by W. H. Meeks III Minimal surfaces of finite topology by W. H. Meeks III and H. Rosenberg Constructions of minimal surfaces by gluing minimal immersions by N. Kapouleas The conformal theory of Alexandrov embedded constant mean curvature surfaces in $\mathbb{R}^3$ by R. Mazzeo, F. Pacard, and D. Pollack Constructing mean curvature 1 surfaces in $H^3$ with irregular ends by W. Rossman, M. Umehara, and K. Yamada Conformal structures and necksizes of embedded constant mean curvature surfaces by R. Kusner Uniqueness of the Riemann minimal surfaces by J. Perez, W. H. Meeks III, and A. Ros The mathematical protein folding problem by Y. Fang Minimal and CMC surfaces obtained by Ribaucour transformations by K. Tenenblat Meromorphic data for surfaces of mean curvature one in hyperbolic space, II by R. Sa Earp and E. Toubiana Special Lagrangian submanifolds by R. Schoen Lectures on special Lagrangian geometry by D. Joyce Variational problems in Lagrangian geometry: $\mathbb{Z}_2$-currents by J. Wolfson Minimal surfaces and the topology of three-manifolds by J. Hass Minimal surfaces in geometric 3-manifolds by J. H. Rubinstein Cousins of constant mean curvature surfaces by K. Grosse-Brauckmann An approach to the Willmore conjecture by P. Topping Minimal surfaces and harmonic maps into singular geometry by C. Mese Shortest networks in 2 and 3 dimensions by J. H. Rubinstein List of participants.