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Global Theory of Minimal Surfaces
Edited by: David Hoffman, Mathematical Sciences Research Institute (MSRI), Berkeley, CA
A co-publication of the AMS and Clay Mathematics Institute.
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Clay Mathematics Proceedings
2005; 800 pp; softcover
Volume: 2
ISBN-10: 0-8218-3587-4
ISBN-13: 978-0-8218-3587-6
List Price: US$131
Member Price: US$104.80
Order Code: CMIP/2
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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.

Titles in this series are co-published 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 genus-one helicoid as a limit of screw-motion 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 Picard-type results for properly immersed minimal surfaces in \(\mathbb{R}^3\)
  • M. Ritoré -- Optimal isoperimetric inequalities for three-dimensional Cartan-Hadamard 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 three-manifolds
  • J. H. Rubinstein -- Minimal surfaces in geometric 3-manifolds
  • K. Große-Brauckmann -- 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
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