期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

平面凸体的等周亏格的上界估计

UPPER BOUND OF ISOPERIMETRIC DEFICIT FOR CONVEX BODY IN THE EUCLIDEAN PLANE
下载PDF
导出
摘要 本文研究平面凸体的等周亏格的上界估计.利用文献[20]中的思想得到一些新的由凸体的周长、面积、最小外接圆半径和最大内切圆半径表示的等周亏格的上界估计,推广了文献[20]中的结果. In this paper, we investigate the upper bound of isoperimetric deficit in the Euclidean plane. Following ideas in [20], we obtain some new upper bounds expressed by perimeter, area, the radius of minimum circumscribed disc and the radius of maximum inscribed disc of a convex body, which generalizes the results of [20].
作者 何刚 姜德烁
机构地区 遵义师范学院数学系 商丘师范学院数学与信息科学学院
出处 《数学杂志》 CSCD 北大核心 2013年第2期349-353,共5页 Journal of Mathematics
基金 国家天元基金(项目号:11126324) 商丘师范学院青年骨干教师资助计划(2011GGJS01)
关键词 等周不等式 BONNESEN型不等式 凸体 等周亏格 isoperimetric inequality Bonnesen-style inequality convex body isoperimetric deficit
分类号 O186.5 [理学—基础数学]
  • 相关文献

参考文献24

  • 1Bonnesen T. Les problems des isoprimtres et des ispiphanes [M]. Paris: Gauthier-Villars, 1929.
  • 2Bonnesen T, Fenchel W. Theorie der Konvexen KSeper [M]. Berlin, New York: Springer-Verlag, 1974.
  • 3任德鳞.积分几何学引论[M].上海:上海科学技术出版社,1988.
  • 4Banchoff T F, Pohl W F. A generalization of the isoperimetric inequality [J]. J. Diff. Geo., 1971, 6: 175-213.
  • 5Bokowski J, Heil E. Integral representation of quermassintegrals and Bonnesemstyle inequalities [J]. Arch. Math., 1986, 47: 79-89.
  • 6Burago Yu D, Zalgaller V A. Geometric inequalities [M]. Berlin, Heidelberg: Springer-Verlag, 1988.
  • 7Diskant V. A generalization of Bonnesen's inequalities [J]. Soviet Math. Dokl., 1973, 14: 1728-1731.
  • 8Gardner R. Geometric tomography [M]. New York: Cambridge Univ. Press, 1995.
  • 9Gysin L. The isoperimetric inequality for nonsimple closed curves [J]. Proc. Amer. Math. Soc., 1993, 118(1): 197 203.
  • 10Osserman R. The isoperimetric inequality [J]. Bull. Amer. Math. Soc., 1978, 84: 1182-1238.

二级参考文献27

  • 1LI Ming & ZHOU JiaZu School of Mathematics and Statistics,Southwest University,Chongqing 400715,China.An isoperimetric deficit upper bound of the convex domain in a surface of constant curvature[J].Science China Mathematics,2010,53(8):1941-1946. 被引量：17
  • 2Osserman R., Bonnesen-style isoperimetric inequality, Amer. Math. Monthly, 1979, 86: 1-29.
  • 3Ren D., Topics in integral geometry, Sigapore: World Scientific, 1994.
  • 4Santalo L. A., Integral geometry and geometric probability, Reading, Mass, Addison-Wesley, 1976.
  • 5Zhou J., On the Willmore deficit of convex surfaces, Lectures in Applied Mathematics of Amer. Math. Soc., 1994, 30: 279-287.
  • 6Hsiang W. Y., An elementary proof of the isoperimetric problem, Ann. of Math., 2002, 23A(1): 7-12.
  • 7Zhang G., A sufficient condition for one convex body containing another, Chin. Ann. of Math., 1988, 4: 447-451.
  • 8Zhang G., Zhou J., Containment measures in integral geometry, Integral geometry and Convexity, Singapore: World Scientific, 2006, 153-168.
  • 9Zhou J., A kinematic formula and analogous of Hadwiger's theorem in space, Contemporary Mathematics, 1992, 140: 159-167.
  • 10Zhou J., The sufficient condition for a convex domain to contain another in R^4, Proc. Amer. Math. Soc., 1994, 212: 907-913.

共引文献52

数学杂志
2013年 第2期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部