## Differential and Integral Equations

- Differential Integral Equations
- Volume 18, Number 2 (2005), 225-232.

### Asymptotic behaviors of star-shaped curves expanding by $V=1-K$

#### Abstract

We consider asymptotic behaviors of star-shaped curves expanding by $V=1-K$, where $V$ denotes the outward-normal velocity and $K$ curvature. In this paper, we show the followings. The difference of the radial functions between an expanding curve and circle has its asymptotic shape as $t\rightarrow+\infty$. For two curves, if the asymptotic shapes are identical, then the curves are also. The set of all asymptotic shapes is dense in $C(S^1)$.

#### Article information

**Source**

Differential Integral Equations, Volume 18, Number 2 (2005), 225-232.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060230

**Mathematical Reviews number (MathSciNet)**

MR2106103

**Zentralblatt MATH identifier**

1212.53094

**Subjects**

Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35B40: Asymptotic behavior of solutions

#### Citation

Yagisita, Hiroki. Asymptotic behaviors of star-shaped curves expanding by $V=1-K$. Differential Integral Equations 18 (2005), no. 2, 225--232. https://projecteuclid.org/euclid.die/1356060230