Two-point functions on Riemannian manifolds (Q1062021)

Let (M,g) be a smooth Riemannian manifold of dimension \(n\geq 2\). A smooth function F on a neighborhood U of the diagonal in \(M\times M\) is called a two-point function if for every (x,y)\(\in U\) there exists a shortest geodesic joining x to y. The authors give the basic elements of the theory of two-point functions and then obtain results with respect to harmonic spaces and spaces with volume-preserving symmetries. The clarity of the paper is noteworthy.