Convexity of the distance function to convex subsets of Riemannian manifolds

S. Khajehpour; M. R. Pouryayevali

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arXiv · 1802.09192

Convexity of the distance function to convex subsets of Riemannian manifolds

S. Khajehpour·M. R. Pouryayevali

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Abstract

A characterization of the proximal normal cone is obtained and a separation theorem for convex subsets of Riemannian manifolds is established. Moreover, the convexity of the distance function $d_S$ for a convex subset $S$ in the cases where the boundary of $S$ contains a geodesic segment, the boundary of $S$ is $C^2$ or the boundary of $S$ is not regular is discussed. Furthermore, a nonsmooth version of positive semi-definiteness of Hessian of convex functions on Riemannian manifolds is established.

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BibTeX RIS

S. Khajehpour, M. R. Pouryayevali. 2018-02-26. Convexity of the distance function to convex subsets of Riemannian manifolds. https://arxiv.org/abs/1802.09192

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