Pure and Applied Mathematics Quarterly

Volume 9 (2013)

Number 3

On the asymptotic stability of stationary lines in the curve shortening problem

Pages: 493 – 506

DOI: https://dx.doi.org/10.4310/PAMQ.2013.v9.n3.a6


Xiao-Liu Wang (Department of Mathematics, Southeast University, Nanjing, China)

Wei-Feng Wo (Department of Mathematics, Ningbo University, Ningbo, China)


The asymptotic stability of the stationary lines in the curve shortening problem was studied in Nara-Taniguchi [NT2] when the initial curve is a graph over the stationary line. The result is extended to a class of nongraphic initial curves.


curve shortening problem, curvature flow, asymptotic behavior, foliation, Sturm oscillation theorem

2010 Mathematics Subject Classification

Primary 53C44. Secondary 35B05, 35B35, 35B40, 53C12.

Published 13 November 2013