| 关于Heisenberg群上的等周不等式 |
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| 引用本文： | 朱新河,王秀芬. 关于Heisenberg群上的等周不等式[J]. 山东理工大学学报：自然科学版, 2006, 20(6): 38-40 |
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| 作者姓名： | 朱新河 王秀芬 |
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| 作者单位： | 天津工业大学,理学院数学系,天津,300160;淄博职业学院,物业管理与消防技术系,山东,淄博,255314 |
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| 摘 要： | 证明了在一维Heisenberg群H1上C-C球不是等周集;同时在A类集中有等周集的假设前提下,给出了Heisenberg群H1上等周不等式的最佳常数.
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| 关 键 词： | Heisenberg群 等周不等式 最佳常数 等周集 |
| 文章编号： | 1672-6197(2006)06-0038-03 |
| 收稿时间： | 2006-03-24 |
| 修稿时间： | 2006-03-24 |
The isoperimetric inequality on the Heisenberg group Hn |
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| ZHU Xin-he,WANG Xiu-fen. The isoperimetric inequality on the Heisenberg group Hn[J]. Journal of Shandong University of Technology:Science and Technology, 2006, 20(6): 38-40 |
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| Authors: | ZHU Xin-he WANG Xiu-fen |
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| Affiliation: | 1. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China; 2. Department of Property Management and Fire protection Technology, Zibo Vocational Institute, Zibo 255314, China |
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| Abstract: | In this paper,we prove that the C-C balls are not isoperimetric sets on the one-dimensional Heisenberg group H~1.Under the hypothesis that there were isoperimetric sets in the class A,we obtain the best constant in the isoperimetric inequality. |
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| Keywords: | Heisenberg group isoperimetric inequality best constant isoperimetric set |
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