Journal of Soviet Mathematics

, Volume 10, Issue 3, pp 395-435

First online:

Sufficient criteria of convexity

  • Yu. D. Burago
  • , V. A. Zalgaller

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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.