Differential and Integral Equations

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

Hiroki Yagisita

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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


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