Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T06:13:37.410Z Has data issue: false hasContentIssue false
  • English
  • Français

VOLUME INEQUALITIES FOR Lp-JOHN ELLIPSOIDS AND THEIR DUALS*

Published online by Cambridge University Press:  01 September 2007

LU FENGHONG  and
LENG GANGSONG
LU FENGHONG
Affiliation:
Department of Mathematics, Shanghai University, Shanghai, 200444, P.R. China. e-mail: lulufh@163.com
LENG GANGSONG
Affiliation:
Department of Mathematics, Shanghai University, Shanghai, 200444, P.R. China. e-mail: lulufh@163.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we establish some inequalities among the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual, which are the strengthened version of known results. We also prove inequalities among the polar of the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual.

Keywords

52A4052A20.
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 3 , September 2007 , pp. 469 - 477
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

REFERENCES

1.Campi, S. and Gronchi, P., The L p-Busemann-Petty centroid inequality, Adv. Math. 167 (2002), 128–141.Google Scholar
2.Firey, W. J., p-means of convex bodies, Math. Scand. 10 (1962), 17–24.CrossRefGoogle Scholar
3.Gardner, R. J., Geometric tomography (Cambridge University Press, 1995).Google Scholar
4.Grinberg, E. and Zhang, G. Y., Convolutions, transforms, and convex bodies, Proc. London Math. Soc. 78 (1999), 77–115.CrossRefGoogle Scholar
5.Haberl, C. and Ludwig, M., A characterization of L p intersection bodies, Int. Math. Res. Notices, to appear.Google Scholar
6.Lutwak, E., The Brunn-Minkowski-Firey theory I: Mixed volumes and the Minkowski problem, J. Differential Geom. 38 (1993), 131–150.Google Scholar
7.Lutwak, E., The Brunn-Minkowski-Firey theory II: Affine and geominimal surface areas, Adv. Math. 118 (1996), 244–294.Google Scholar
8.Lutwak, E. and Zhang, G., Blaschke-Santaló inequalities, J. Differential Geom. 47 (1997), 1–16.Google Scholar
9.Lutwak, E., Yang, D. and Zhang, G. Y., L p affine isoperimetric inequalities, J. Differential Geom. 56 (2000), 111–132.Google Scholar
10.Lutwak, E., Yang, D. and Zhang, G. Y., A new ellipsoid associated with conves bodies, Duke Math. J. 104 (2000), 375–390.Google Scholar
11.Lutwak, E., Yang, D. and Zhang, G. Y., L p John ellipsoids, Proc. London Math. Soc. (3) 90 (2005), 497–520.CrossRefGoogle Scholar
12.Meyer, M. and Werner, E., On the p–affine surface area, Adv. Math. 152 (2000), 288–313.Google Scholar
13.Ryabogin, D. and Zvavitch, A., The Fourier transform and Firey projections of convex bodies, Indiana. Univ. Math. J. 53 (2004), 667–682.Google Scholar
14.Schneider, R., Convex Bodies: The Brunn-Minkowski theory (Cambridge University Press, 1993).Google Scholar
15.Yu, W., Leng, G. and Wu, D., Dual L p-John ellipsoids, Proc. Edinburgh Math. Soc. (2), to appear.Google Scholar