, Volume 10, Issue 3, pp 395-435

Sufficient criteria of convexity

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Abstract

In this article a survey of criteria of convexity of sets and hypersurfaces inR n, in Riemannian and infinite-dimensional linear spaces, is made. Included are the following sections: support property; local convexity; local support; curvature of the boundary; section by planes; uniqueness of closest points; systems of sets.

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 45, pp. 3–52, 1974.