10-2016
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.
@misc{isoperimetric-inequality,
author = {Dylan Cant},
title = {A curvature flow and applications to an isoperimetric inequality},
year = {2016},
eprint = {1610.05844},
archivePrefix = {arXiv},
primaryClass = {math.DG},
}