A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points. (28th August 2014) - Kılıcman, Adem; Saleh, Wedad
Abstract : LetW n beC ∞ complete, simply connected n -dimensional Riemannian manifolds without conjugate points. Assume thatS ⊂ W 2 is starshaped wherek e r S ≠ S . For every pointx ∈ S ∖ k e r S, defineA ( x ) = { y : y lies on some geodesic segment in S from x to a point of ker S } . There is a finite collectionA of all maximalA sets whose union is S . Further, kerS = ∩ { A: A inA } .