On a Logarithmic Type Nonlocal Plane Curve Flow

Abstract

In this paper the author devotes to studying a logarithmic type nonlocal plane curve flow. Along this flow, the convexity of evolving curve is preserved, the perimeter decreases, while the enclosed area expands. The flow is proved to exist globally and converge to a finite circle in the C ^∞ metric as time goes to infinity.

Keywords

Convex curve / Nonlocal flow / Logarithmic type / Parallel curve