Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (1): 180-188.doi: 10.1007/s10473-025-0114-x
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Xinbao Lu1, Ge Xiong1,*, Jiangyan Tao2
Received:
2024-09-04
Published:
2025-02-06
Contact:
*Ge Xiong, E-mail,: xiongge@tongji.edu.cn
About author:
Xinbao Lu, E-mail,: xinbaolu@tongji.edu.cn; Jiangyan Tao, E-mail,: taojiangyan@zjnu.edu.cn
Supported by:
CLC Number:
Xinbao Lu, Ge Xiong, Jiangyan Tao. ON LEGENDRE AND LYZ ELLIPSOIDS[J].Acta mathematica scientia,Series B, 2025, 45(1): 180-188.
[1] Ball K. Volume ratios and a reverse isoperimetric inequality. J London Math Soc, 1991, 44: 351-359 [2] Ball K. Ellipsoids of maximal volume in convex bodies. Geom Dedicata, 1992, 41: 241-250 [3] Böröczky K, Lutwak E, Yang D, Zhang G. Affine images of isotropic measures. J Differential Geom, 2015, 99: 407-442 [4] Bourgain J. On high-dimensional maximal functions associated to convex bodies. Amer J Math, 1986, 108: 1467-1476 [5] Giannopoulos A, Papadimitrakis M. Isotropic surface area measures. Mathematika, 1999, 46: 1-13 [6] Gardner R. Geometric Tomography. Cambridge: Cambridge University Press, 2006 [7] Gruber P. Convex and Discrete Geometry. Berlin: Springer, 2007 [8] Gruber P. John and Loewner ellipsoids. Discrete Comput Geom, 2011, 46: 776-788 [9] Hu J, Xiong G. The logarithmic John ellipsoid. Geom Dedicata, 2018, 197: 33-48 [10] John F. Extremum problems with inequalities as subsidiary conditions// Studies and Essays Presented to R. Courant on his 60th Birthday. New York: Interscience Publishers, 1948: 187-204 [11] Klartag B. On John-type ellipsoids// Milman V, Schechtman G. Geometric Aspects of Functional Analysis. Berlin: Springer, 2004: 149-158 [12] Leichtweiss K. Affine Geometry of Convex Bodies. Heidelberg: Johann Ambrosius Barth Verlag, 1998 [13] Lewis D. Ellipsoids defined by Banach ideal norms. Mathematika, 1979, 26: 18-29 [14] Lindenstrauss J, Milman V. The local theory of normed spaces and its applications to convexity// Gruber P, Wills J. Handbook of Convex Geometry. Amsterdam: North-Holland, 1993: 1149-1220 [15] Lu X, Xiong G. The Lp John ellipsoids for negative indices. Israel J Math, 2023, 255: 155-176 [16] Ludwig M. Ellipsoids and matrix-valued valuations. Duke Math J, 2003, 119: 159-188 [17] Lutwak E, Yang D, Zhang G. A new ellipsoid associated with convex bodies. Duke Math J, 2000, 104: 375-390 [18] Lutwak E, Yang D, Zhang G. A new affine invariant for polytopes and Schneider's projection problem. Trans Amer Math Soc, 2001, 353: 1767-1779 [19] Lutwak E, Yang D, Zhang G. The Cramer-Rao inequality for star bodies. Duke Math J, 2002, 112: 59-81 [20] Lutwak E, Yang D, Zhang G. Lp John ellipsoids. Proc London Math Soc, 2005, 90: 497-520 [21] Lutwak E, Yang D, Zhang G. A volume inequality for polar bodies. J Differential Geom, 2010, 84: 163-178 [22] Milman V, Pajor A. Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space// Lindenstrauss J, Milman V. Geometric Aspects of Functional Analysis, Lecture Notes in Math 1376. Berlin: Springer, 1989: 64-104 [23] Pisier G. The Volume of Convex Bodies and Banach Space Geometry. Cambridge: Cambridge University Press, 1989 [24] Schneider R. Convex Bodies: The Brunn-Minkowski Theory. Cambridge: Cambridge University Press, 2014 [25] Zhu B, Zhou J, Xu W. Dual Orlicz-Brunn-Minkowski theory. Adv Math, 2014, 264: 700-725 [26] Zou D, Xiong G. Orlicz-John ellipsoids. Adv Math, 2014, 265: 132-168 [27] Zou D, Xiong G. Orlicz-Legendre ellipsoids. J Geom Anal, 2016, 26: 2474-2502 [28] Zou D, Xiong G. Convex bodies with identical John and LYZ ellipsoids. Int Math Res Not, 2018: 470-491 |
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