## Soliton solutions to the curve shortening flow on the sphere

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- by Hiuri Fellipe Santos dos Reis and Keti Tenenblat PDF
- Proc. Amer. Math. Soc.
**147**(2019), 4955-4967 Request permission

## Abstract:

It is shown that a curve on the unit sphere is a soliton solution to the curve shortening flow if and only if its geodesic curvature is proportional to the inner product between its tangent vector and a fixed vector of $\mathbb {R}^3$. Using this characterization, we describe the geometry of such a curve on the sphere, we study its qualitative behavior, and we prove the convergence of the curve to the equator orthogonal to the fixed vector.## References

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## Additional Information

**Hiuri Fellipe Santos dos Reis**- Affiliation: Department of Mathematics, Universidade de Brasília, 70910-900, Brasília-DF, Brazil
- MR Author ID: 1287830
- Email: hiuri.reis@ifg.edu.br
**Keti Tenenblat**- Affiliation: Department of Mathematics, Universidade de Brasília, 70910-900, Brasília-DF, Brazil
- MR Author ID: 171535
- Email: K.Tenenblat@mat.unb.br
- Received by editor(s): December 10, 2018
- Received by editor(s) in revised form: February 9, 2019, and February 22, 2019
- Published electronically: June 10, 2019
- Additional Notes: The first author was partially supported by CNPq Proc. 141275/2014-6, Ministry of Science and Technology, Brazil

The second author was partially supported by CNPq Proc. 312462/2014-0, Ministry of Science and Technology, Brazil and FAPDF/Brazil grant 0193.001346/2016. - Communicated by: Jiaping Wang
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 4955-4967 - MSC (2010): Primary 53C44
- DOI: https://doi.org/10.1090/proc/14607
- MathSciNet review: 4011527