Points joined by three shortest paths on convex surfaces
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- by Tudor Zamfirescu PDF
- Proc. Amer. Math. Soc. 123 (1995), 3513-3518 Request permission
Abstract:
Let S be a convex surface and $x \in S$. It is shown here that the set of all points of S joined with x by at least three shortest paths can be dense in S. It is proven that, in fact, in the sense of Baire categories most convex surfaces have this property, for any x. Moreover, on most convex surfaces, for most of their points, there is just one farthest point (in the intrinsic metric), and precisely three shortest paths lead to that point.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3513-3518
- MSC: Primary 52A15; Secondary 53C45
- DOI: https://doi.org/10.1090/S0002-9939-1995-1273530-9
- MathSciNet review: 1273530