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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
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ISBN-13
978-0-8218-4116-7 (9780821841167)
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Schweitzer Klassifikation
Minimization of length, area, and volume. Some solved and some unsolved problems in the theory of minimal graphs and surfaces by A. T. Fomenko The Steiner problem for convex boundaries, I: The general case by A. O. Ivanov and A. A. Tuzhilin The Steiner problem for convex boundaries, II: The regular case by A. O. Ivanov and A. A. Tuzhilin Effective calibrations in the theory of minimal surfaces by L. H. Van Minimal cones invariant under adjoint actions of compact Lie groups by I. S. Novikova Global properties of minimal surfaces in ${\mathbb R}^3$ and ${\mathbb H}^3$ and their Morse type indices by A. A. Tuzhilin Calibration forms and new examples of globally minimal surfaces by A. O. Ivanov Ruled special Lagrangian surfaces by A. Borisenko Functional-topological properties of the Plateau operator and applications to the study of bifurcations in problems of geometry and hydrodynamics by A. Yu. Borisovich Harmonic maps into Lie groups and the multivalued Novikov functional by A. V. Tyrin.
