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Minimal Surfaces
Edited by: A. T. Fomenko
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Advances in Soviet Mathematics
1993; 342 pp; hardcover
Volume: 15
ISBN-10: 0-8218-4116-5
ISBN-13: 978-0-8218-4116-7
List Price: US$167
Member Price: US$133.60
Order Code: ADVSOV/15
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This book contains recent results from a group focusing on minimal surfaces in the Moscow State University seminar on modern geometrical methods, headed by A. V. Bolsinov, A. T. Fomenko, and V. V. Trofimov. The papers collected here fall into three areas: one-dimensional minimal graphs on Riemannian surfaces and the Steiner problem, two-dimensional minimal surfaces and surfaces of constant mean curvature in three-dimensional Euclidean space, and multidimensional globally minimal and harmonic surfaces in Riemannian manifolds. The volume opens with an exposition of several important problems in the modern theory of minimal surfaces that will be of interest to newcomers to the field. Prepared with attention to clarity and accessibility, these papers will appeal to mathematicians, physicists, and other researchers interested in the application of geometrical methods to specific problems.

Readership

Mathematicians, physicists, and other researchers interested in the application of geometrical methods to specific problems.

Table of Contents

  • A. T. Fomenko -- Minimization of length, area, and volume. Some solved and some unsolved problems in the theory of minimal graphs and surfaces
  • A. O. Ivanov and A. A. Tuzhilin -- The Steiner problem for convex boundaries, I: The general case
  • A. O. Ivanov and A. A. Tuzhilin -- The Steiner problem for convex boundaries, II: The regular case
  • L. H. Vân -- Effective calibrations in the theory of minimal surfaces
  • I. S. Novikova -- Minimal cones invariant under adjoint actions of compact Lie groups
  • A. A. Tuzhilin -- Global properties of minimal surfaces in \({\mathbb R}^3\) and \({\mathbb H}^3\) and their Morse type indices
  • A. O. Ivanov -- Calibration forms and new examples of globally minimal surfaces
  • A. Borisenko -- Ruled special Lagrangian surfaces
  • A. Yu. Borisovich -- Functional-topological properties of the Plateau operator and applications to the study of bifurcations in problems of geometry and hydrodynamics
  • A. V. Tyrin -- Harmonic maps into Lie groups and the multivalued Novikov functional
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