About the error term for best approximation with respect to the Hausdorff related metrics

Discrete and Computational Geometry

Volumn 25, Issue 2, 2001, Pages 293-309

  Boroczky K ^a  

^a INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039298674     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004540010088     Document Type: Article

References (17)

1. L. V. Ahlfors: Lectures on Quasiconformal Mappings. Van Nostrand, Princeton, NJ, 1966.
2. U. Betke, M. Henk, and J. M. Wills: A new approach to covering. Mathematika, 42:251-263, 1995.
3. W. Blaschke: Affine Differentialgeometrie. Springer-Verlag, Berlin, 1923.
4. K. Falconer: Fractal Geometry. Wiley, New York, 1990.
5. G. Fejes Tóth: The loosest packing of the sphere by circles. M.Sc. thesis, Roland Eötvös University, Budapest, 1970 (in Hungarian).
6. L. Fejes Töth: Lagerungen in der Ebene, auf der Kugel und im Raum, 2nd edn. Springer-Verlag, Berlin, 1972.
7. P. M. Gruber: Asymptotic estimates for best and stepwise approximation of convex bodies, I. Forum Math., 5:281-297, 1993.
8. P. M. Gruber: Aspects of approximation of convex bodies. In: Handbook of Convex Geometry A, pp. 319-345. North-Holland, Amsterdam, 1993.
9. P. M. Gruber: Comparisons of best and random approximation of convex bodies by polytopes. Rend. Circ. Mat. Palermo, 50:189-216, 1997.
10. O. Lehto: Univalent Functions and Teichmüller Spaces. Springer-Verlag, Berlin, 1987.
11. K. Leichtweiß: Affine Geometry of Convex Bodies. Johann Ambrosius Barth Verlag, Heidelberg, 1998.
12. M. Ludwig: Asymptotic approximation of convex curves: the Hausdorff metric case. Arch. Math., 70:331-336, 1998.
13. D. E. McClure and R. A. Vitale: Polygonal approximation of plane convex bodies. J. Math. Anal. Appl., 51:326-358, 1975.
14. R. Schneider: Zur optimalen Approximation konvexer Hyperflächen durch Polyeder. Math. Ann., 256: 289-301, 1979.
15. R. Schneider: Convex Bodies: the Brunn-Minkowski Theory. Cambridge University Press, Cambridge, 1993.
16. S. Tabachnikov: On the dual billiard problem. Adv. in Math., 115:221-249, 1995.
17. B. L. van der Waerden: Punkte auf der Kugel. Drei Zusatze. Math. Ann., 125:213-222, 1952.