| 摘要: |
| 本文研究了常曲率平面Xκ中一域包含另一域的包含问题.利用积分几何中包含测度理论及对称等周亏格,得到了Xκ中一域包含另一域的充分条件,并给出Xκ中等周不等式的一个简化证明. |
| 关键词: 基本运动公式 常曲率平面 等周亏格 等周不等式 |
| DOI： |
| 分类号:O186.5 |
| 基金项目:贵州省科学技术基金项目(黔科合J字LKZS[2012]12号). |
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| SUFFICIENT CONDITIONS FOR A DOMAIN TO CONTAIN ANOTHER DOMAIN IN A SURFACE OF CONSTANT CURVATURE |
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CHEN Ming, HE Gang
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School of Mathematics and Computing Science, Zunyi Normal College, Zunyi 563002, China
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| Abstract: |
| In this paper,we investigate the containment problem in a surface Xκ of constant curvature κ.Using the symmetric isoperimetric deficit and following the idea of containment measure in integral geometry,we establish some sufficient conditions for D0 ⊂ gD1 or D0 ⊃ gD1 and give an simplified proof of the isoperimetric inequality in Xκ. |
| Key words: kinematic fundamental formula surface of constant curvature isoperimetric deficit isoperimetric inequality |
