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- W1614003815 abstract "We prove that on a complete Riemannian manifold $M$ of dimension $n$ with sectional curvature $K_M < 0$, two points which realize a local maximum for the distance function (considered as a function of two arguments) are connected by at least $2n+1$ geodesic segments. A simpler version of the argument shows that if one of the points is fixed and $K_M leq 0$ then the two points are connected by at least $n+1$ geodesic segments. The proof uses mainly the convexity properties of the distance function for metrics of negative curvature." @default.
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- W1614003815 date "1997-01-01" @default.
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- W1614003815 title "On the number of geodesic segments connecting two points on manifolds of non-positive curvature" @default.
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