Quantitative characterizations of nonconvex bodies with smooth boundaries in Hilbert spaces via the metric projection

摘要

The present paper is a continuation of a previous work with conditions for regularity of the metric projection. Here we provide a full quantitative characterization of closed bodies in Hilbert spaces with Cp+1-smooth boundary in terms of the smoothness of the metric projection and the behavior of its first derivative. (C) 2020 Elsevier Inc. All rights reserved.