Multi-dimensional variational methods in the topology of extremals

Abstract

CONTENTS § 1. Introduction § 2. The multi-dimensional volume functional, local and global minimality of surfaces in a Riemannian manifold § 3. Multi-dimensional variational problems and extraordinary (co)homology theories § 4. Methods for an effective construction of globally minimal surfaces in Riemannian manifolds § 5. Three geometrical problems in the calculus of variations § 6. Harmonic maps of spheres in non-trivial homotopy classes References