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Article overview
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Short closed geodesics with self-intersections | Viveka Erlandsson
; Hugo Parlier
; | Date: |
1 Sep 2016 | Abstract: | 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 $k$. | Source: | arXiv, 1609.0217 | Services: | Forum | Review | PDF | Favorites |
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