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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.
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참고문헌 (11)
참고문헌 신청
E. Lutwak / 1975 / A general Bieberbach inequality / Math. Proc. Cambridge Philos. Soc. 78 (3) : 493 ~ 495
E. Lutwak / 1975 / Width-integrals of convex bodies / Proc. Amer. Math. Soc. 53 (2) : 435 ~ 439
E. Lutwak / 1977 / Mixed width-integrals of convex bodies / Israel J. Math. 28 (3) : 249 ~ 253
E. Lutwak / 1985 / Mixed projection inequalities / Trans. Amer. Math. Soc. 287 (1) : 91 ~ 105
E. Lutwak / 1993 / Inequalities for mixed projection bodies / Trans. Amer. Math. Soc. 339 (2) : 901 ~ 916
E. Lutwak / 1975 / Width-integrals of convex bodies / Proc. Amer. Math. Soc. 53 (2) : 435 ~ 439
E. Lutwak / 1977 / Mixed width-integrals of convex bodies / Israel J. Math. 28 (3) : 249 ~ 253
E. Lutwak / 1985 / Mixed projection inequalities / Trans. Amer. Math. Soc. 287 (1) : 91 ~ 105
E. Lutwak / 1993 / Inequalities for mixed projection bodies / Trans. Amer. Math. Soc. 339 (2) : 901 ~ 916
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