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A general Bieberbach inequality

Published online by Cambridge University Press:  24 October 2008

Erwin Lutwak
Affiliation:
Columbia University

Extract

A proof is given of a general Bieberbach inequality which has the Bieberbach, Urysohn and harmonic Urysohn inequalities as special cases. This establishes a stronger as well as more general inequality than the previously mentioned inequalities. Generalizations (as well as strengthened versions) of other inequalities previously proven by the author are also obtained.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Bieberbach, L.Über eine extremaleigenschaft des kreises. Jber. Deutsch. Math.-Verein 24 (1915), 247250.Google Scholar
(2)Hadwiger, H.Vorlesungen über Inhalt, Oberfläche und Isoperimetrie (Berlin, Springer, 1957).Google Scholar
(3)Hardy, G. H., Littlewood, J. E. and Polya, G.Inequalities (Cambridge University Press, 1934).Google Scholar
(4)Lutwak, E.Dual mixed volumes. Pacific J. Math. (To appear.)Google Scholar
(5)Lutwak, E. Mean dual and harmonic cross-sectional measures. (To appear.)Google Scholar
(6)Santaló, L.Un invariante afin para los cuerpos convexos del espacio de n dimentiones. Portugal Math. 8 (1949), 155161.Google Scholar
(7)Urysohn, P.Mean width and volume of convex bodies in n dimensional space. Rec. Math. Soc. Math. Moscow 31 (1924), 477486. (Russian.)Google Scholar