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For convex bodies, chord power integrals were introduced
and studied in several papers (see [3], [6], [14], [15], etc.). The aim of
this article is to study them further, that is, we establish the Brunn-
Minkowski-type inequalities and get the upper bound for chord power
integrals of convex bodies. Finally, we get the famous Zhang projection
inequality as a corollary. Here, it is deserved to mention that we make
use of a completely distinct method, that is using the theory of inclusion
measure, to establish the inequality.
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참고문헌 (15)
참고문헌 신청
A. D. Alexandrov / 1938 / On the theory of mixed volumes of convex bodies / mathematics of the USSR-Sbornik 3 (45) : 28 ~ 46
D. Ren / 1988 / An Introduction to Integral Geometry / Science and Technology Press
G. D. Chakerian / 1967 / Inequalities for the difference body of a convex body / Proc. Amer. Math. Soc. : 879 ~ 884
G. Xiong / 2003 / Intersection bodies and inclusion measures of convex bodies / Journal of Mathematics Wuhan University 23 (1) : 6 ~ 10
G. Xiong / 2007 / Inclusion measures of convex bodies / Journal of Mathematical Research Experience 27 (1) : 81 ~ 86
D. Ren / 1988 / An Introduction to Integral Geometry / Science and Technology Press
G. D. Chakerian / 1967 / Inequalities for the difference body of a convex body / Proc. Amer. Math. Soc. : 879 ~ 884
G. Xiong / 2003 / Intersection bodies and inclusion measures of convex bodies / Journal of Mathematics Wuhan University 23 (1) : 6 ~ 10
G. Xiong / 2007 / Inclusion measures of convex bodies / Journal of Mathematical Research Experience 27 (1) : 81 ~ 86
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