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Short closed geodesics with self-intersections
Mathematical Proceedings of the Cambridge Philosophical Society ( IF 0.8 ) Pub Date : 2020-01-24 , DOI: 10.1017/s030500411900032x VIVEKA ERLANDSSON , HUGO PARLIER
Mathematical Proceedings of the Cambridge Philosophical Society ( IF 0.8 ) Pub Date : 2020-01-24 , DOI: 10.1017/s030500411900032x VIVEKA ERLANDSSON , HUGO PARLIER
Our main point of focus is the set of closed geodesics on hyperbolic surfaces. For any fixed integer k , we are interested in the set of all closed geodesics with at least k (but possibly more) self-intersections. Among these, we consider those of minimal length and investigate their self-intersection numbers. We prove that their intersection numbers are upper bounded by a universal linear function in k (which holds for any hyperbolic surface). Moreover, in the presence of cusps, we get bounds which imply that the self-intersection numbers behave asymptotically like k for growing k .
中文翻译:
具有自相交的短闭合测地线
我们的主要关注点是双曲曲面上的一组封闭测地线。对于任何固定整数ķ ,我们对所有闭合测地线的集合感兴趣,至少ķ (但可能更多)自相交。其中,我们考虑那些最小长度的并研究它们的自交数。我们证明了它们的交点数是由一个通用线性函数在ķ (适用于任何双曲曲面)。此外,在存在尖点的情况下,我们得到的界限意味着自交数的行为渐近ķ 为了成长ķ .
更新日期:2020-01-24
中文翻译:
具有自相交的短闭合测地线
我们的主要关注点是双曲曲面上的一组封闭测地线。对于任何固定整数