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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new flow on starlike curves in $\mathbb{R}^3$


Authors: Rongpei Huang and David A. Singer
Journal: Proc. Amer. Math. Soc. 130 (2002), 2725-2735
MSC (2000): Primary 53A04; Secondary 53A15
Published electronically: April 11, 2002
MathSciNet review: 1900890
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Abstract: In this note we find a new evolution equation for starlike curves in $\mathbb{R}^3$. We study the evolution of the subaffine curvature and subaffine torsion under the flow and show that it is completely integrable. The solutions to the evolution which move without changing affine shape are subaffine elastic curves. We integrate the subaffine elastica by quadratures.


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Additional Information

Rongpei Huang
Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200062, People’s Republic of China
Email: rphuang@math.ecnu.edu.cn

David A. Singer
Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106-7058
Email: das5@po.cwru.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06631-5
PII: S 0002-9939(02)06631-5
Received by editor(s): February 4, 2000
Published electronically: April 11, 2002
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2002 American Mathematical Society