  In this paper, the isoperimetric inequality in centro-affine plane geometry
is obtained. We also investigate the long-term behavior of an invariant plane
curve flow, whose evolution process can be expressed as a second-order
nonlinear parabolic equation with respect to centro-affine curvature. The
forward and backward limits in time are discussed, which shows that a closed
convex embedded curve may converge to an ellipse when evolving according to
this flow.
