| 摘要: |
| 本文主要研究平面卵形线的曲率积分不等式.利用积分几何中凸集的支持函数以及外平行集的性质,得到了Gage等周不等式与曲率的熵不等式的一个积分几何的简化证明;进一步地,我们得到了一个新的关于曲率积分的不等式. |
| 关键词: 曲率 Gage等周不等式 熵不等式 支持函数 |
| DOI： |
| 分类号:O186.5 |
| 基金项目:重庆师范大学基金项目资助(12XLB026). |
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| SOME NOTES ON CURVATURE INTEGRAL INEQUALITIES |
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MA Lei1, ZENG Chun-na2
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1.Dept. of Math., Gaozhou Normal College, Guangdong University of Petrochemical Technology, Maoming 525200, China;2.College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China
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| Abstract: |
| In this paper we investigate the curvature integral inequalities. Using the properties of support functions of convex set and the outer parallel set in integral geometry, we give a simplified proof of the Gage-isoperimetric inequality and the entropy inequality for curvature. Finally, we obtain a new integral inequality for curvature. |
| Key words: curvature the Gage-isoperimetric inequality entropy inequality support function. |
