Proceedings of the American Mathematical Society

Author(s): Rongpei Huang; David A. Singer
Journal: Proc. Amer. Math. Soc. 130 (2002), 2725-2735.
MSC (2000): Primary 53A04; Secondary 53A15
Posted: April 11, 2002
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53A04, 53A15

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: 10.1090/S0002-9939-02-06631-5
PII: S 0002-9939(02)06631-5
Received by editor(s): February 4, 2000
Posted: April 11, 2002
Communicated by: Wolfgang Ziller
Copyright of article: Copyright 2002, American Mathematical Society

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