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

DOI:
https://doi.org/10.1090/S0002-9939-2012-11745-9

Published electronically:
September 19, 2012

MathSciNet review:
3020863

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-2012-11745-9

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