Abstract
LetWnbeC∞complete, simply connectedn-dimensional Riemannian manifolds without conjugate points. Assume thatS⊂W2is starshaped wherekerS≠S. For every pointx∈S∖kerS, defineA(x)={y:ylies on some geodesic segment inSfromxto a point of kerS}. There is a finite collectionAof all maximalAsets whose union isS. Further, kerS=∩{A:AinA}.
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