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| 球面上的等周问题 |
| On the Isoperimetric Inequality for Circle |
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| DOI：10.3969/j.issn.1671-5322.2008.04.004 |
| 中文关键词: 等周 曲率 测地曲率 挠率 |
| 英文关键词: isoperimetric inequality curvature geodesic curvature torsion |
| 基金项目: |
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| 中文摘要: |
| ∑是球面,∑上有一定长为L的简单闭曲线C.对于等周曲线C围成的区域D的面积,通过引入辅助函数:φ(t,λ)=Area(D)+λ(L-∫LO|R'(s,t)|ds),根据拉普拉斯定理、曲率、测地曲率和挠率得曲线为圆时,围成的面积最大. |
| 英文摘要: |
| Let ∑ be a sphere in R3.A simple closed curve C of length L encloses domain D of area A on ∑.Using auxiliary function (t,λ)=Area(D)+λ(L-∫0L|R′(s,t)|ds),laplace’s theorema,curvature,geodesic curvature and torsion,we get the inequality A2≤4π2-L2 that area is biggest when the curve is a circle. |
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