A Note on Starshaped Sets in 2-Dimensional Manifolds without Conjugate Points. (28th August 2014)

• Record Type: Journal Article
• Authors: Kılıcman, Adem; Saleh, Wedad
• Other Names: Mursaleen M. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-08-28
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/675735
• Languages: English
• ISSNs: 2314-8896

Abstract

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 } .