Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T13:36:32.645Z Has data issue: false hasContentIssue false

Conjugate points on convex surfaces

Published online by Cambridge University Press:  26 February 2010

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

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.

Type
Research Article
Copyright
Copyright © University College London 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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), 314.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 (19871988), 314350.CrossRefGoogle Scholar
7.Zamfirescu, T.. Many endpoints and few interior points of geodesies. Invent. Math., 69 (1982), 253257.CrossRefGoogle Scholar
8.Zamfirescu, T.. Nearly all convex surfaces are smooth and strictly convex. Mh. Math., 103 (1987), 5762.CrossRefGoogle Scholar
9.Zamfirescu, T.. Porosity in convexity. Real Analysis Exch., 15 (19891990), 424436.Google Scholar
10.Zamfirescu, T.. Baire categories in convexity. Atti Sent. Mat. Fis. Univ. Modena, 39 (1991), 279304.Google Scholar