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# Communications in Analysis and Geometry

## Volume 18 (2010)

### Number 1

### Contracting convex immersed closed plane curves with fast speed of curvature

Pages: 23 – 75

DOI: http://dx.doi.org/10.4310/CAG.2010.v18.n1.a2

#### Authors

#### Abstract

We study the contraction of a convex immersed plane curve along its normalvector direction with speed function $\frac{1}{\alpha}k^{\alpha}$, where$k>0$ is the curvature of the evolving curve and $\alpha>1$ is aconstant. We show that the blow-up rate of the curvature is always of*type one* and the rescaled solution will converge to a limit that mayor may not be degenerate.