  Long time existence and convergence to a circle is proved for radial graph
solutions to a mean curvature type curve flow in warped product surfaces (under
a weak assumption on the warp potential of the surface). This curvature flow
preserves the area enclosed by the evolving curve, and this fact is used to
prove a general isoperimetric inequality applicable to radial graphs in warped
product surfaces under weak assumptions on the warp potential.
