Clay Mathematics Proceedings 2005; 800 pp; softcover Volume: 2 ISBN10: 0821835874 ISBN13: 9780821835876 List Price: US$131 Member Price: US$104.80 Order Code: CMIP/2
 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 mathematiciansundergraduates, postdoctoral students, young researchers, and world expertsparticipated in the most extensive meeting ever held on the subject in its 250year 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 constantmeancurvature submanifolds, geometric measure theory and the doublebubble 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 threedimensional manifolds. The wide variety of topics covered make this volume suitable for graduate students and researchers interested in differential geometry. Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA). Readership Graduate students and research mathematicians interested in differential geometry. Table of Contents  F. Morgan and M. Ritoré  Geometric measure theory and the proof of the double bubble conjecture
 M. Weber  Classical minimal surfaces in Euclidean space by examples: Geometric and computational aspects of the Weierstrass representation
 K. Polthier  Computational aspects of discrete minimal surfaces
 R. Schoen  Mean curvature in Riemannian geometry and general relativity
 H. Karcher  Introduction to conjugate Plateau constructions
 J. Pérez and F. J. López  Parabolicity and minimal surfaces
 A. Ros  The isoperimetric problem
 M. Wolf  Flat structures, Teichmüller theory and handle addition for minimal surfaces
 M. Weber, D. Hoffman, and M. Wolf  The genusone helicoid as a limit of screwmotion invariant helicoids with handles
 D. Hoffman  Computing minimal surfaces
 J. Spruck  Geometric aspects of the theory of fully nonlinear elliptic equations
 H. Karcher  Hyperbolic surfaces of constant mean curvature one with compact fundamental domains
 J. Choe  Isoperimetric inequalities of minimal submanifolds
 F. Martín  Complete nonorientable minimal surfaces in \(\mathbb{R}^3\)
 F. J. López  Some Picardtype results for properly immersed minimal surfaces in \(\mathbb{R}^3\)
 M. Ritoré  Optimal isoperimetric inequalities for threedimensional CartanHadamard manifolds
 T. H. Colding and W. P. Minicozzi II  Embedded minimal disks
 M. Traizet  Construction of minimal surfaces by gluing Weierstrass representations
 W. H. Meeks III  Global problems in classical minimal surface theory
 W. H. Meeks III and H. Rosenberg  Minimal surfaces of finite topology
 N. Kapouleas  Constructions of minimal surfaces by gluing minimal immersions
 R. Mazzeo, F. Pacard, and D. Pollack  The conformal theory of Alexandrov embedded constant mean curvature surfaces in \(\mathbb{R}^3\)
 W. Rossman, M. Umehara, and K. Yamada  Constructing mean curvature 1 surfaces in \(H^3\) with irregular ends
 R. Kusner  Conformal structures and necksizes of embedded constant mean curvature surfaces
 J. Pérez, W. H. Meeks III, and A. Ros  Uniqueness of the Riemann minimal surfaces
 Y. Fang  The mathematical protein folding problem
 K. Tenenblat  Minimal and CMC surfaces obtained by Ribaucour transformations
 R. Sa Earp and E. Toubiana  Meromorphic data for surfaces of mean curvature one in hyperbolic space, II
 R. Schoen  Special Lagrangian submanifolds
 D. Joyce  Lectures on special Lagrangian geometry
 J. Wolfson  Variational problems in Lagrangian geometry: \(\mathbb{Z}_2\)currents
 J. Hass  Minimal surfaces and the topology of threemanifolds
 J. H. Rubinstein  Minimal surfaces in geometric 3manifolds
 K. GroßeBrauckmann  Cousins of constant mean curvature surfaces
 P. Topping  An approach to the Willmore conjecture
 C. Mese  Minimal surfaces and harmonic maps into singular geometry
 J. H. Rubinstein  Shortest networks in 2 and 3 dimensions
 List of participants
