Convexity of the distance function to convex subsets of Riemannian manifolds

2018/02/26 by Khajehpour, S., Pouryayevali, M. R.
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.09192

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 C² 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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