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In this paper we derive some basic inequalities connecting the Minkowski measure of symmetry, the Minkowski symmetral and the Banach-Mazur distance. We then explore the geometric contents of these inequalities and shed light on the structure of the quotient $\cb/{\rm Aff}$ of the space of convex bodies modulo the affine transformations.
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참고문헌 (10)
참고문헌 신청
B. Grunbaum / 1963 / Measures of symmetry for convex sets, convexity / Proceedings of the Symposium in Pure Mathematics VII:233~270
Q. Guo / 2005 / Stability of the Minkowski measure of asymmetry for convex bodies / Discrete and Computational Geometry 34:351~362
Q. Guo / 2002 / On asymmetry of some convex bodies / Discrete Comput. Geom. 27(2):239~247
Q. Guo / 2003 / Approximation of convex bodies by convex bodies / Northeast Math. 19(4):323~332
F. John / 1948 / Extremum problems with inequalities as subsidiary conditions, Courant Anniversary Volume / Interscience :187~204
Q. Guo / 2005 / Stability of the Minkowski measure of asymmetry for convex bodies / Discrete and Computational Geometry 34:351~362
Q. Guo / 2002 / On asymmetry of some convex bodies / Discrete Comput. Geom. 27(2):239~247
Q. Guo / 2003 / Approximation of convex bodies by convex bodies / Northeast Math. 19(4):323~332
F. John / 1948 / Extremum problems with inequalities as subsidiary conditions, Courant Anniversary Volume / Interscience :187~204
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