Download the PDF of the paper entitled “Efficient Geodesic Super Efficiency on Complex Curves” by Xifeng Jin and William W. Menasco.

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overview: We show that efficient geodesics have a powerful property of ‘super-efficiency’. For any two vertices $v , w \in \mathcal{C}(S_g)$ in the complex curve of the closed oriented surface of genus $g \geq 2 $ and any efficient geodesic $v = v_1 , \cdots , v_{\text d}=w$ , but explicitly computable maximum $v_1$ vertex candidates. In this memo, we establish the bounds of this computable list, independent of ${\text d}$- distance and dependent only on genus (super efficient trait). The proof is based on a new intersection growth inequality between the number of curve intersections and the distance in a compound curve, and an exhaustive analysis of dot graphs associated with intersection sequences.

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Source: William W. Menasco [view email]


Friday 21 August 2020 20:01:07 UTC (251 KB)


Thursday, May 27, 2021 17:32:13 UTC (283 KB)


Tuesday, June 14, 2022 19:18:32 UTC (1,581 KB)


Tuesday, May 23, 2023 17:36:15 UTC (935 KB)

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