A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points - Adem Kılıcman; Wedad Saleh (Journal of Function Spaces)
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∈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}.