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Conjugate points on convex surfaces

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Tudor Zamfirescu
Tudor Zamfirescu
Affiliation:
Fachbereich Mathematik, Universität Dortmund, Postfach 50 05 00, D-4600 Dortmund 50, Germany.
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Extract

On a convex surface S ⊂ Rd, two points x, y are conjugate if there are at least two shortest paths, called segments, from x to y. This paper is about the set of points conjugate to some fixed point xєS.

MSC classification

Secondary: 52A15: Convex sets in $3$ dimensions (including convex surfaces)
Type
Research Article
Information
Mathematika , Volume 38 , Issue 2 , December 1991 , pp. 312 - 317
Copyright
Copyright © University College London 1991

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References

1.Aleksandrov, A. D.. Die innere Geometrie der konvexen Flachen (Akademie-Verlag, Berlin, 1955).Google Scholar
2.Busemann, H.. Convex Surfaces (Interscience Publishers, New York, 1958).Google Scholar
3.Cullen, H. F.. Introduction to General Topology (D. C. Heath ' Co, Boston, 1967).Google Scholar
4.Dolzenko, E.. Boundary properties of arbitrary functions. Izv. Akad. Nauk SSSR Ser. Mat., 31 (1967), 3–14.Google Scholar
5.Gruber, P.. Geodesies on typical convex surfaces. Atti Accad. Naz. Lincei Rend. Cl. Sci. riz. Mat. Natur. (8). To appear.Google Scholar
6.Zajíček, L.. Porosity and σ-porosity. Real Analysis Exch., 13 (1987–1988), 314–350.CrossRefGoogle Scholar
7.Zamfirescu, T.. Many endpoints and few interior points of geodesies. Invent. Math., 69 (1982), 253–257.CrossRefGoogle Scholar
8.Zamfirescu, T.. Nearly all convex surfaces are smooth and strictly convex. Mh. Math., 103 (1987), 57–62.CrossRefGoogle Scholar
9.Zamfirescu, T.. Porosity in convexity. Real Analysis Exch., 15 (1989–1990), 424–436.Google Scholar
10.Zamfirescu, T.. Baire categories in convexity. Atti Sent. Mat. Fis. Univ. Modena, 39 (1991), 279–304.Google Scholar