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R^n中的一个Bonnesen型不等式

A Bonnesen-Style Inequality in the Euclidean Space R^n
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摘要 研究了n维欧氏空间中凸体K的等周亏格的下界估计,即Bonnesen型不等式.首先加强了Lutwak中得到的关于凸体K的p-平均不等式,用此得到一个用凸体K的均质积分及调和均质积分表示的等周亏格的下界估计. In this paper, we investigate the lower bound of isoperimetric deficit, that is, the Bonnesen-style inequality, for a convex body K in the Euclidean space Rn. Firstly we strength the inequality obtained by Lutwak, then we get a Bonnesen-style inequality expressing by quermassintegrale and harmonics quermassintegrale of the convex body K.
作者 李泽清 侯林波 徐文学
机构地区 毕节学院数学与计算机科学学院 黄河科技学院民族学院 西南大学数学与统计学院
出处 《数学的实践与认识》 北大核心 2015年第21期210-214,共5页 Mathematics in Practice and Theory
基金 贵州省科学技术基金项目(2012gz10256) 中央高校基本业务费专项资金资助(XDJK2014C164)
关键词 等周不等式 等周亏格 BONNESEN型不等式 JENSEN不等式 isoperimetric inequality isoperimetric deficit Bonnesen-style inequality Jenseninequality
分类号 O186.5 [理学—基础数学]
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参考文献16

  • 1Bonnesen T. Les problems des isoperimetres et des isepiphanes[M]. Paris, Gauthier-Villars, 1929.
  • 2Bonnesen T, Fenchel W. Theorie der konvexen KSrper [M].Berlin, New York, 1974.
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二级参考文献22

  • 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.

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数学的实践与认识
2015年 第21期

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