Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Soliton solutions to the curve shortening flow on the sphere


Authors: Hiuri Fellipe Santos dos Reis and Keti Tenenblat
Journal: Proc. Amer. Math. Soc. 147 (2019), 4955-4967
MSC (2010): Primary 53C44
DOI: https://doi.org/10.1090/proc/14607
Published electronically: June 10, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53C44

Retrieve articles in all journals with MSC (2010): 53C44


Additional Information

Hiuri Fellipe Santos dos Reis
Affiliation: Department of Mathematics, Universidade de Brasília, 70910-900, Brasília-DF, Brazil
Email: hiuri.reis@ifg.edu.br

Keti Tenenblat
Affiliation: Department of Mathematics, Universidade de Brasília, 70910-900, Brasília-DF, Brazil
Email: K.Tenenblat@mat.unb.br

DOI: https://doi.org/10.1090/proc/14607
Keywords: Curve shortening flow, solitons solutions
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
Article copyright: © Copyright 2019 American Mathematical Society