A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points

Let wn be c∞ complete,simply connected n-dimensional riemannian manifolds without conjugate points. assume that s ⊂ w2 is starshaped where kers ≠ s. for every point x ε s kers,define a(x) = {y: y lies on some geodesic segment in s from x to a point of kers}. there is a finite collection a of all maximal a sets whose union is s. further,kers = ∩{a : a in a}. copyright © 2014 a. kilicman and w. saleh.