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The Steiner point of a closed hypersurface

Published online by Cambridge University Press:  26 February 2010

Harley Flanders
Harley Flanders
Affiliation:
University College, London
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Let C be a compact convex set in En, not necessarily containing interior points. The Steiner point of K has been defined (see Shephard [6]) as

Type
Research Article
Information
Mathematika , Volume 13 , Issue 2 , December 1966 , pp. 181 - 188
Copyright
Copyright © University College London 1966

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References

1. Gericke, H., “Über stützbare Flächen und ihre Entwicklung nach Kugelfunktionen”, Math. Zeitschrift, 46 (1940), 55–61.CrossRefGoogle Scholar
2. Grünbaum, B., “Measures of symmetry for convex sets”, Proc. Symposia in Pure Math. VII, American Math. Soc. (1963), 233–270, esp. 238ff.CrossRefGoogle Scholar
3. Grünbaum, B., Convex polytopes, Wiley & Sons, New York (forthcoming), ¬¬14.3, 14.4.CrossRefGoogle Scholar
4. Kubota, T., “Über die Sehwerpunkte der konvexen geschlossenen Kurven und Flächen”, Tóhoku Math. J., 14 (1918), 20–27.Google Scholar
5. Sallee, G. T., “A valuation property of Steiner points”, Mathematika, 13 (1966), 76–82.CrossRefGoogle Scholar
6. Shephard, G. C., “Approximation problems for convex polyhedra”, Mathematika, 11 (1964), 9–18.Google Scholar
7. Shephard, G. C., “The Steiner point of a convex polytope “, Canadian J. of Math. (to appear).Google Scholar
8. Steiner, J., Von den Krümmungsschwerpunkte ebener Curven, Journal fur die Beine und Angew. Math., 21 (1840), 33–63, 101–122 (= Gesammelte Werke, Band 2 (1882), 99–159).Google Scholar
9. Su, B., “On Steiner's curvature-centroid”, Japan. J. of Math.”, 4 (1927), 195–201.CrossRefGoogle Scholar
10. Chern, S. S., “A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds”, Annals of Math., 45 (1944), 747–752.Google Scholar
11. Flanders, H., “Development of an extended exterior differential calculus”, Trans. American Math. Soc., 75 (1953), 311–326, esp. 323 ff.CrossRefGoogle Scholar
12. Flanders, H., Differential forms (Academic Press: New York, 1963), esp. 38–44, 112–126.Google Scholar
13. Chern, S. S., “Integral formulas for hypersurfaces in Euclidean space and their applications to uniqueness theorems”, J. of Math, and Mech., 8 (1959), 947–955Google Scholar