MIXED BRIGHTNESS-INTEGRALS OF CONVEX BODIES
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초록
The mixed width-integrals of convex bodies are defined by E. Lutwak. In this paper, the mixed brightness-integrals of convex bodies are defined. An inequality is established for the mixed brightness-integrals analogous to the Fenchel-Aleksandrov inequality for the mixed volumes. An isoperimetric inequality (involving the mixed brightness-integrals) is presented which generalizes an inequality recently obtained by Chakerian and Heil. Strengthened version of this general inequality is obtained by introducing indexed mixed brightness-integrals.
Abstract
The mixed width-integrals of convex bodies are defined by E. Lutwak. In this paper, the mixed brightness-integrals of convex bodies are defined. An inequality is established for the mixed brightness-integrals analogous to the Fenchel-Aleksandrov inequality for the mixed volumes. An isoperimetric inequality (involving the mixed brightness-integrals) is presented which generalizes an inequality recently obtained by Chakerian and Heil. Strengthened version of this general inequality is obtained by introducing indexed mixed brightness-integrals.
참고문헌 (11)
- G. D. Chakerian, "Isoperimetric inequalities for the mean width of a convex body", Geometriae Dedicata, 1(3), pp.356~362 (1973)
- G. D. Chakerian, "The mean volume of boxes and cylinders circumscribed about a convex body", Israel J. Math., 12, pp.249~256 (1972)
- R. J. Gardner, "Geometric Tomography, Encyclopedia of Mathematics and its Applications, 58" (1995), Cambridge University Press
- H. Hardy, "Inequalities, Reprint of the 1952 edition. Cambridge Mathematical Library" (1988), Cambridge University Press
- F. Lu, "Mixed chord-integral of star bodies, preprint", ~ (2007)
- E. Lutwak, "Width-integrals of convex bodies", Proc. Amer. Math. Soc., 53(2), pp.435~439 (1975)
- E. Lutwak, "A general Bieberbach inequality", Math. Proc. Cambridge Philos. Soc., 78(3), pp.493~495 (1975)
- E. Lutwak, "Mixed width-integrals of convex bodies", Israel J. Math., 28(3), pp.249~253 (1977)
- E. Lutwak, "Mixed projection inequalities", Trans. Amer. Math. Soc., 287(1), pp.91~105 (1985)
- E. Lutwak, "Inequalities for mixed projection bodies", Trans. Amer. Math. Soc., 339(2), pp.901~916 (1993)
- R. Schneider, "Convex Bodies: the Brunn-Minkowski theory, Encyclopedia of Mathematics and its Applications, 44" (1993), Cambridge University Press