Variational Principles of Topology Multidimensional Minimal Surface Theory [Paperback]

1. Simplest Classical Variational Problems.- ?1 Equations of Extremals for Functionals.- ?2 Geometry of Extremals.- 2.1. The Zero-Dimensional and One-Dimensional Cases.- 2.2. Some Examples of the Simplest Multidimensional Functional. The Volume Functional.- 2.3. The Classical Plateau Problem in Dimension 2.- 2.4. The Second Fundamental Form on the Riemannian Submanifold.- 2.5. Local Minimality.- 2.6. First Examples of Globally Minimal Surfaces.- 2. Multidimensional Variational Problems and Extraordinary (Co)Homology Theory.- ?3 The Multidimensional Plateau Problem and Its Solution in the Class of Mapping on Spectra of Manifolds with Fixed Boundary.- 3.1. The Classical Formulations (Finding the Absolute Minimum).- 3.2. The Classical Formulations (Finding a Relative Minimum).- 3.3. Difficulties Arising in the Minimization of the Volume Functional volk for k > 2. Appearance on Nonremovable Strata of Small Dimensions.- 3.4. Formulations of the Plateau Problem in the Language of the Usual Spectral Homology.- 3.5. The Classical Multidimensional Plateau Problem (the Absolute Minimum) and the Language of Bordism Theory.- 3.6. Spectral Bordism Theory as an Extraordinary Homology Theory.- 3.7. The Formulation of the Solution to the Plateau Problem (Existence of the Absolute Minimum in Spectral Bordism Classes).- ?4 Extraordinary (Co)Homology Theories Determined for Surfaces with Singularities.- 4.1. The Characteristic Properties of (Co)Homology Theories.- 4.2. Extraordinary (Co)Homology Theories for Finite Cell Complexes.- 4.3. The Construction of Extraordinary (Co)Homology Theories for Surfaces with Singularities (on Compact Sets).- 4.4. Verifying the Characteristic Properties of the Constructed Theories.- 4.5. Additional Properties of Extraordinary Spectral Theories.- 4.6. Reduced (Co)Homology Groups on Surfaces with Singularities.- ?5 The Coboundary and Boundary of a Pair of Spaces (X, A).- 5.1. The Coboundary of a Pair (X,A).- 5.2. The Boundary of a Pair (X,A).- lS(