2017
Том 69
№ 9

All Issues

On the number of critical submanifolds of a function on a manifold

Bondar' O. P.

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Abstract

We consider differentiable functions on a manifold such that the set of their critical points is a disconnected union of smooth submanifolds. A topological characteristic of the manifold is introduced; in terms of this characteristic, we estimate the least possible number of critical submanifolds of these functions.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 12, pp 1915-1919.

Citation Example: Bondar' O. P. On the number of critical submanifolds of a function on a manifold // Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1702–1705.

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