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Busemann–Petty Problems for General L_p-Intersection Bodies 被引量：5

Busemann–Petty Problems for General L_p-Intersection Bodies
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摘要 For 0 〈 p 〈 1, Haberl and Ludwig defined the notions of symmetric Lp-intersection body and nonsymmetric Lp-intersection body. In this paper, we introduce the general Lp-intersection bodies. Furthermore, the Busemann-Petty problems for the general Lp-intersection bodies are shown. For 0 〈 p 〈 1, Haberl and Ludwig defined the notions of symmetric Lp-intersection body and nonsymmetric Lp-intersection body. In this paper, we introduce the general Lp-intersection bodies. Furthermore, the Busemann-Petty problems for the general Lp-intersection bodies are shown.
作者 Wei Dong WANG Ya Nan LI
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第5期777-786,共10页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China(Grant No.11371224) Foundation of Degree Dissertation of Master of China Three Gorges University(Grant No.2014PY067)
关键词 General Lp-intersection body Busemann-Petty problem General Lp-intersection body, Busemann-Petty problem
分类号 O18 [理学—基础数学]
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参考文献20

  • 1Berck, G.: Convexity of Lp-intersection bodies. Adv. Math., 222(3), 920-936 (2009).
  • 2Gardner, R. J.: A positive answer to the Busemann-Petty problem in three dimensions. Ann. of Math., 140(2), 435-447 (1994).
  • 3Gardner, R. J.: Geometric Tomography, 2nd edition, Cambridge Univ. Press, Cambridge, 2006.
  • 4Gardner, R. J., Koldobsky, A., Schlumprecht, T.: An analytic solution to the Busemann-Petty problem on sections of convex bodies. Ann. of Math., 149(2), 691—703 (1999).
  • 5Goodey, P., Weil, W.: Intersection bodies and ellipsoids. Mathematika, 42(2), 295-304 (1995).
  • 6Haberl, C.: Lp intersection bodies. Adv. Math., 217(6), 2599-2624 (2008).
  • 7Haberl, C., Ludwig, M.: A characterization of Lp intersection bodies. International Mathematics Research Notices, Art. ID 10548 (2006).
  • 8Hardy, G. H., Littlewood, J. E., Polya G.: Inequalities, Cambridge University Press, Cambridge, 1959.
  • 9Kalton, N. J., Koldobsky, A.: Intersection bodies and Lp spaces. Adv. Math., 196, 257-275 (2005).
  • 10Koldobsky, A.: Intersection bodies and the Busemann-Petty problem. C. R. Acad. Sci. Paris Ser. I Math., 325(11), 1181-1186 (1997).

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Acta Mathematica Sinica,English Series
2015年 第5期

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