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

Authors

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

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

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

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

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