Existence of curves with constant geodesic curvature in a Riemannian 2-sphere
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- by Da Rong Cheng and Xin Zhou PDF
- Trans. Amer. Math. Soc. 374 (2021), 9007-9028 Request permission
Abstract:
We prove the existence of immersed closed curves of constant geodesic curvature in an arbitrary Riemannian 2-sphere for almost every prescribed curvature. To achieve this, we develop a min-max scheme for a weighted length functional.References
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Additional Information
- Da Rong Cheng
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- MR Author ID: 1243846
- ORCID: 0000-0002-4675-3839
- Email: drcheng@uwaterloo.ca
- Xin Zhou
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853; and Department of Mathematics, University of California Santa Barbara, Santa Barbara, California 93106
- Email: xinzhou@cornell.edu
- Received by editor(s): February 26, 2021
- Received by editor(s) in revised form: June 20, 2021
- Published electronically: September 16, 2021
- Additional Notes: The second author was partially supported by NSF grant DMS-1811293, DMS-1945178, and an Alfred P. Sloan Research Fellowship.
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 9007-9028
- MSC (2020): Primary 58E10
- DOI: https://doi.org/10.1090/tran/8510
- MathSciNet review: 4337936