Weber’s problem on the Riemannian Manifolds: Some upper bounds for the minimun Weber’s function

Abstract

In this paper we obtain some upper bounds for the minimum of the Weber function on a strongly convex ball in a Riemannian manifold with positive sectional curvature; where the minimum is reached on the weighted geometric median of “m” given points in the strongly convex.

Keywords

• The Weber problema
• Weighted Geometric Median
• Riemannian manifold
• Strongly convex set