Calibration forms and new examples of stable and globally minimal surfaces

A. O. Ivanov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: This paper is devoted to the development of methods of investigating the stability and global minimality of specific surfaces in Euclidean space and more generally in the Riemannian manifold. The author has obtained an effective sufficient condition for the stability of symmetric cones of any codimension in Euclidean space. By means of this sufficient condition he has proved the stability of several new series of cones of codimension two and higher. The author has constructed a new class of globally minimal surfaces in locally trivial vector bundles. The proof of the basic theorems is carried out by means of the construction of suitable calibration forms.

UDC: 514.77

MSC: Primary 53A10, 49Q05; Secondary 53C65

Received: 09.11.1989

 English version: Mathematics of the USSR-Sbornik, 1992, 71:2, 289–308

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