Pure and Applied Mathematics Quarterly
Volume 9 (2013)
On the asymptotic stability of stationary lines in the curve shortening problem
Pages: 493 – 506
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.