Minimal Surfaces ( Advances in Soviet Mathematics )

Publication series ： Advances in Soviet Mathematics

Author： A. T. Fomenko  

Publisher： American Mathematical Society‎

Publication year： 2018

E-ISBN: 9781470446123

P-ISBN(Paperback): 9780821841167

Subject： O186.16 differential geometry in large

Keyword： 数学

Language： ENG

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Minimal Surfaces

Description

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.

Chapter

Cover

Title page

Contents

Editor’s Foreword

Minimization of length, area, and volume. Some solved and some unsolved problems in the theory of minimal graphs and surfaces

The Steiner problem for convex boundaries, I: the general case

The Steiner problem for convex boundaries, II: the regular case

Effective calibrations in the theory of minimal surfaces

Minimal cones invariant under adjoint actions of compact Lie groups

Global properties of minimal surfaces in 𝑅³ and 𝐻³ and their Morse type indices

Calibration forms and new examples of globally minimal surfaces

Ruled special Lagrangian surfaces

Functional-topological properties of the Plateau operator and applications to the study of bifurcations in problems of geometry and hydrodynamics

Harmonic maps into Lie groups and the multivalued Novikov functional

Back Cover

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