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

 

On a planar area-preserving curvature flow


Authors: Xiao-Li Chao, Xiao-Ran Ling and Xiao-Liu Wang
Journal: Proc. Amer. Math. Soc. 141 (2013), 1783-1789
MSC (2010): Primary 53C44; Secondary 35B40, 35K59, 37B25
Published electronically: September 19, 2012
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Abstract: A classical nonlocal curvature flow preserving the enclosed area is reinvestigated. The uniform upper bound and lower bound of curvature are established for the first time. As a result, a detailed proof is presented for the asymptotic behavior of the flow.


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Additional Information

Xiao-Li Chao
Affiliation: Department of Mathematics, Southeast University, Nanjing, People’s Republic of China

Xiao-Ran Ling
Affiliation: Department of Mathematics, Southeast University, Nanjing, People’s Republic of China

Xiao-Liu Wang
Affiliation: Department of Mathematics, Southeast University, Nanjing, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11745-9
PII: S 0002-9939(2012)11745-9
Keywords: Mean curvature flow, nonlocal flow, asymptotic behavior
Received by editor(s): August 24, 2011
Published electronically: September 19, 2012
Additional Notes: This work was supported by PRC Grants NSFC 11101078, 10971029 and 11171064 and the Natural Science Foundation of Jiangsu Province BK2011583
Communicated by: Lei Ni
Article copyright: © Copyright 2012 American Mathematical Society