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Self-Crossing Geodesics

  • Mathematical Gems and Curiosities
  • Sophie Morier-Genoud and Valentin Ovsienko, Editors
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References

  1. S. Angenent. Curve shortening and the topology of closed geodesics on surfaces. Ann. of Math. (2) 162:3 (2005), 1187–1241.

  2. V. I. Arnold. Remarks on the enumeration of plane curves. In Topology of Real Algebraic Varieties and Related Topics, Amer. Math. Soc. Transl. Ser. 2, vol. 173, pp. 17–32. American Mathematical Society, 1996.

  3. A. Petrunin and S. Zamora Barrera. What is differential geometry: curves and surfaces. arXiv:2012.11814, 2020.

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Acknowledgments

I want to thank Maxim Arnold, Serge Tabachnikov, and Sergio Zamora Barrera for their help. This work was partially supported by NSF grant DMS-2005279 and Simons Foundation grant 584781.

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Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA

    Anton Petrunin

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  1. Anton Petrunin
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Correspondence to Anton Petrunin.

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Petrunin, A. Self-Crossing Geodesics. Math Intelligencer 43, 16–18 (2021). https://doi.org/10.1007/s00283-021-10127-0

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