Self-similar curve shortening flow in hyperbolic 2-space
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- by Eric Woolgar and Ran Xie
- Proc. Amer. Math. Soc. 150 (2022), 1301-1319
- DOI: https://doi.org/10.1090/proc/15770
- Published electronically: January 5, 2022
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Abstract:
We find and classify self-similar solutions of the curve shortening flow in standard hyperbolic 2-space. Together with earlier work of Halldorsson on curve shortening flow in the plane and Santos dos Reis and Tenenblat in the 2-sphere, this completes the classification of self-similar curve shortening flows in the constant curvature model spaces in 2-dimensions.References
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Bibliographic Information
- Eric Woolgar
- Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada; and Theoretical Physics Institute, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
- MR Author ID: 252050
- Email: ewoolgar@ualberta.ca
- Ran Xie
- Affiliation: Department of Statistics, Stanford University, Stanford, California 94305-4020
- ORCID: 0000-0002-5483-7266
- Email: ranxie@stanford.edu
- Received by editor(s): February 11, 2021
- Received by editor(s) in revised form: June 21, 2021
- Published electronically: January 5, 2022
- Additional Notes: The first author was supported by NSERC Discovery Grant RGPIN–2017–04896
- Communicated by: Guofang Wei
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 1301-1319
- MSC (2020): Primary 53C42
- DOI: https://doi.org/10.1090/proc/15770
- MathSciNet review: 4375723