PM  >> Vol. 2 No. 4 (October 2012)

    Stability in the Busemann-Petty Problem for Arbitrary Measures

  • 全文下载: PDF(220KB) HTML    PP.221-225   DOI: 10.12677/PM.2012.24034  
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汪 卫:湖南科技大学数学与计算科学学院

Busemann-Petty问题星体凸体Radon变换The Busemann-Petty Problem; Star Bodies; Convex Bodies; Radon Transform



Zvavitch found a generalization of the Busemann-Petty problem to arbitrary measures. In this paper, we study the stability in the Busemann-Petty problem for arbitrary measures by using Radon transform. As application, we obtain a hyperplane inequality for arbitrary measures in dimensions up to four. These results are consistent with Koldobsky’s results which are obtained by using Fourier transform.

汪卫. 一般测度Busemann-Petty问题的稳定性[J]. 理论数学, 2012, 2(4): 221-225.


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