Mean projections and finite packings of convex bodies
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Abstract
Consider the convex hullQ ofn non-overlapping translates of a convex bodyC inE d ,n be large. IfQ has minimali-dimensional projection, 1≤i<d then we prove thatQ is approximately a sphere.
1991 Mathematics Subject Classification
52C17 52A39Preview
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References
- [1]Betke, U., Gritzmann, P., Wilis, J. M.: Slices of L. Fejes Tóth's Sausage Conjecture.Mathematika 29, 194–201 (1982).Google Scholar
- [2]Betke, U., Henk, M., Wills, J. M.: Finite and Infinite Packings. J. Reine Angew. Math. To appear.Google Scholar
- [3]Böröczky, K. Jr., Henk, M.: Radii and the Sausage Conjecture. Canadian Bulletin of Math. (1994). Accepted.Google Scholar
- [4]Conway, J. H., Solane, N. J. A.: Sphere Packings, Lattices and Groups. Berlin: Springer. 1988.Google Scholar
- [5]Fuglede, B.: Stability in the isoperimetric problem for convex or nearly spherical domains inR n. Trans. Amer. Math. Soc.314, 619–638 (1989).Google Scholar
- [6]Groemer, H., Schneider, R.: Stability estimates for some geometric inequalities. Bull. London Math. Soc.23, 67–74 (1971).Google Scholar
- [7]Gruber, P. M., Lekkerkerker, C. G.: Geometry of Numbers. Amsterdam: North-Holland. 1987.Google Scholar
- [8]Henk, M.: Personal communication. (1993).Google Scholar
- [9]Osserman, R.: Bonnesen-style isoperimetric inequalities. Amer. Math. Monthly86, 1–29 (1979).Google Scholar
- [10]Pisier, G.: The Volume of Convex Bodies and Banach Space Geometry. Cambridge: University Press. 1989.Google Scholar
- [11]Kleinschmidt, P., Pachner, U., Wills, J. M.: On L. Fejes Tóth's ‘Sausage Conjecture’. Israel J. Math.47, 216–226 (1984).Google Scholar
- [12]Rogers, C. A.: Packing and Covering Cambridge: University Press. 1964.Google Scholar
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