Classification of balanced sets and critical points of even functions on spheres

Coffman, Charles V.

doi:10.1090/S0002-9947-1991-1007802-0

Classification of balanced sets and critical points of even functions on spheres
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by Charles V. Coffman PDF

Trans. Amer. Math. Soc. 326 (1991), 727-747 Request permission

Abstract:

The Lyusternik-Schnirelman approach to the study of critical points of even functionals on the sphere ${S^N}$ employs min-max or max-min principles whose formulation uses a numerical invariant that is defined for compact balanced subsets of ${S^N}$. The Krasnosel’skii genus is an example. Here we study a general class of such invariants (which is quite large) with particular attention to the following questions: formulation of dual variational principles, multiplicity results for critical points, and determination of the Morse index of nondegenerate critical points.

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