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http://dx.doi.org/10.4134/JKMS.2006.43.3.609

THE MONOTONY PROPERTIES OF GENERALIZED PROJECTION BODIES, INTERSECTION BODIES AND CENTROID BODIES  

Yu, Wu-Yang (Department of Mathematics Shanghai University)
Wu, Dong-Hua (Department of Mathematics Shanghai University)
Publication Information
Journal of the Korean Mathematical Society / v.43, no.3, 2006 , pp. 609-622 More about this Journal
Abstract
In this paper, we established the monotony properties of generalized projection bodies $II_{\imath}K$, intersection bodies $I_{\imath}K$ and centroid bodies ${\Gamma}_{\imath}K$.
Keywords
projection bodies; intersection bodies; centroid bodies; quermassintegrals; dual quermassintegrals; monotony properties;
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1 R. J. Gardner, Intersection bodies and the Busemann-Petty problem, Trans. Amer. Math. Soc. 342 (1994), no. 1, 435-445   DOI   ScienceOn
2 C. M. Petty, Projection bodies, in:'Proceedings of a Colloquium on Convexity', Co- qenhagen, 1965, 234-241, Kobenhavns Univ. Mat. Inst. 1967
3 W. Rudin, Principles of mathematical analysis, McGraw-Hill Companies, Inc. 1976
4 R. Schneider, Convex bodies: the Brunn-Minkowski theory, Encyclopedia of Mathematics and its Applications 44, Cambridge University Press, Cambridge, 1993
5 G. C. Shephard, Shadow systems of convex bodies, Israel J. Math. 2 (1964), 229-236   DOI
6 G. Zhang, Dual kinematic formulas, Trans. Amer. Math. Soc. 351 (1999), no. 3, 985-995   DOI   ScienceOn
7 G. Zhang, A positive solution to the Busemann-Petty problem in $\mathbb{R}^4$, Ann. of Math. 149 (1999), no. 2, 535-543   DOI
8 G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, Cambridge, 1952
9 G. D. Chakerian and E. Lutwak, Bodies with similar projections, Trans. Amer. Math. Soc. 349 (1997), no. 5, 1811-1820   DOI   ScienceOn
10 E. Lutwak, The Brunn-Minkowski-Firey theory I: Mixed volumes and the Minkowski problem, J. Differential Geom. 38 (1993), no. 1, 131-150   DOI
11 C. M. Petty, Centroid surfaces, Pacific J. Math. 11 (1961), 1535-1547   DOI
12 E. Lutwak, On quermassintegrals of mixed projection bodies, Geometriae Dedicata, 33 (1990), no. 1, 51-58
13 E. Lutwak and G. Zhang, Blaschke-Santalo inequalities, J. Differential Geom. 47 (1997), no. 1, 1-16   DOI
14 R. J. Gardner, Geometric Tomography, Encyclopedia of Mathematics and its Applications 58, Cambridge University Press, Cambridge, 1995
15 S. Helgason, The Radon transform, Second edition, Progress in Mathematics, Vol. 5, Birkhauser, Boston, 1999
16 K. Leichtweib, Konvexe mengen, Springer-Verlag, Berlin-New York, 1980
17 E. Lutwak, Dual mixed volumes, Pacific J. Math. 58 (1975), no. 2, 531-538   DOI
18 E. Lutwak, Mixed projection inequalities, Trans. Amer. Math. Soc. 287 (1985), no. 1, 91-105   DOI
19 E. Lutwak, Intersection bodies and dual mixed volumes, Adv. Math. 71 (1988), no. 2, 232-261   DOI
20 E. Lutwak, Centroid bodies and dual mixed volumes, Proc. London Math. Soc. 60 (1990), no. 3, 365-391
21 R. Schneider, Zur einem Problem von Shephard uber die Projektionen konvexer Korper, Math. Z. 101 (1967), 71-82   DOI
22 R. J. Gardner, A positive answer to the Busemann-Petty problem in three dimensions, Ann. of Math. 140 (1994), no. 2, 435-447   DOI
23 G. Zhang, Sections of convex bodies, Amer. J. Math. 118 (1996), no. 2, 319-340   DOI
24 G. Zhang, Centered bodies and dual mixed volumes, Trans. Amer. Math. Soc. 345 (1994), no. 2, 777-801   DOI   ScienceOn