Tietze-type theorem in 2-dimensional Riemannian manifolds without conjugate points

Abstract

Let A be an open connected subset of a C(infinity) complete simply connected 2-dimensional Riemannian manifold without conjugate points W(2). The main result of this short article states that: a point x of A has a local maximal visibility if and only if x is a point of the convex kernel of A. Thus we obtain a Tietze-type theorem in W(2).