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THE PLANE ISOPERIMETRIC PROBLEM FROM THE POINT OFINTEGRAL GEOMETRY

THE PLANE ISOPERIMETRIC PROBLEM FROM THE POINT OFINTEGRAL GEOMETRY
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摘要 We are going to discuss the classical isoperimetric problem via integral geometry. Some new ideas and results are introduced. These ideas and methods may be applied to higher dimensions. We are going to discuss the classical isoperimetric problem via integral geometry. Some new ideas and results are introduced. These ideas and methods may be applied to higher dimensions.
作者 JIAZU ZHOU( School of Mathematics and Statistics, Southwest University, Chongqing 400715)
出处 《黔东南民族职业技术学院学报（综合版）》 2009年第3期1-7,共7页 Journal of Southeast Guizhou Vocational College of Technology for Nationalities(Comprehensive Edition)
基金 Supported in part by Chinese NSF(grant number:10671159)
关键词 CONVEX INEQUALITY dimensions CURVATURE DEFICIT MAT
分类号 O186.5 [理学—基础数学]
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参考文献11

  • 1J. Zhou.On Bonnesen -type inequalities[].Acta Mathematica Sinica.2007
  • 2J. Zhou.Plane Bonnesen -type ineualities[].Acta Mathematica Sinica.2006
  • 3项武义.等周问题的一个初等证明[J].数学年刊（A辑）,2002,23(1):7-12. 被引量：12
  • 4Jia-zu ZHOU School of Mathematics and Statistics, Southwest University, Chongqing 400715, China,Department of Mathematics, Polytechnic University, Brooklyn, NY 11201, USA.The Willmore functional and the containment problem in R^4[J].Science China Mathematics,2007,50(3):325-333. 被引量：9
  • 5G. Zhang,J. Zhou.Containment measures in integral geometry[].Integral ge- ometry and Convexity.2005
  • 6M. Li,J. Zhou.The isoperimetric deficit upper bound for the convex set in a surface of constant curvature[]..
  • 7J. Zhou,L. Ma.The Upper Bound of the Isoperimetric Deficit[]..
  • 8J. Zhou,C. Zhou,F. Ma.Isoperimetric Deficit upper limit of a planar convex set[]..
  • 9J. Zhou,L. Zhao.The Bonnesen -style Isoperimetric Deficit Upper Bound[]..
  • 10Zhou J,Jiang D,Li M,Chen F.Ros’s theorem on hypersufaces[].Acta Mathematica Sinica.2009

二级参考文献2

  • 1Peter Li,Shing-Tung Yau.A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces[J].Inventiones Mathematicae.1982(2)
  • 2H. hadwiger.überdeckung ebener Bereiche durch Kreise und Quadrate[J].Commentarii Mathematici Helvetici.1940(1)

共引文献19

黔东南民族职业技术学院学报（综合版）
2009年 第3期

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