理论数学  >> Vol. 2 No. 4 (October 2012)

一般测度Busemann-Petty问题的稳定性
Stability in the Busemann-Petty Problem for Arbitrary Measures

DOI: 10.12677/PM.2012.24034, PDF, HTML, 下载: 2,595  浏览: 8,981  国家自然科学基金支持

作者: 汪 卫:湖南科技大学数学与计算科学学院

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

摘要: 基于ZvavitchBusemann-Petty问题推广到了一般测度,本文利用Radon变换研究了一般测度Busemann-Petty问题的稳定性。作为应用,我们建立了n(n≤4)维空间中的一个关于一般测度的超截面不等式。这些结果与Koldobsky利用Fourier变换证明的结论是一致的。
Abstract: 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.

文章引用: 汪卫. 一般测度Busemann-Petty问题的稳定性[J]. 理论数学, 2012, 2(4): 221-225. http://dx.doi.org/10.12677/PM.2012.24034

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