Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Points joined by three shortest paths on convex surfaces


Author: Tudor Zamfirescu
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 52A15, 53C45

Retrieve articles in all journals with MSC: 52A15, 53C45


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1273530-9
Keywords: Baire categories, generic convex surfaces, geodesic segments
Article copyright: © Copyright 1995 American Mathematical Society