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

Abstract EN

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}.