A Note on Collars of Simple Closed Geodesics
A Note on Collars of Simple Closed Geodesics
复制标题
关于简单闭合测地线项圈的注解
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
H. Parlier
中科院分区：
文献类型：
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作者：
H. Parlier
对于紧致双曲黎曼曲面，衣领定理给出了简单封闭测地线与所有其他不与初始测地线相交的简单封闭测地线之间距离的下界。这里显示有两种可能的配置，并且在每种配置中都有一个与简单封闭测地线相关的自然领宽。如果将简单封闭测地线α的自然环扩展ε >0，则该扩展环包含无穷多条不与α相交的简单封闭测地线。
For compact hyperbolic Riemann surfaces, the collar theorem gives a lower bound on the distance between a simple closed geodesic and all other simple closed geodesics that do not intersect the initial geodesic. Here it is shown that there are two possible configurations, and in each configuration there is a natural collar width associated to a simple closed geodesic. If one extends the natural collar of a simple closed geodesic α by ε >0, then the extended collar contains an infinity of simple closed geodesics that do not intersect α.