On semiconvexity and weak semiconvexity

Tetiana Osipchuk

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arXiv · 1711.04757

On semiconvexity and weak semiconvexity

Tetiana Osipchuk

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Abstract

Properties of two classes of generally convex sets in the n-dimentional real Euclidean space, called m-semiconvex and weakly m-semiconvex, 1<=m<n, are investigated in the present work. In particular, it is established that an open set with smooth boundary in the plan which is weakly 1-semiconvex but not 1-semiconvex consists minimum of four simply connected components.

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Tetiana Osipchuk. 2017-11-13. On semiconvexity and weak semiconvexity. https://arxiv.org/abs/1711.04757

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