A volume preserving flow and the isoperimetric problem in warped product   spaces
  In this article, we continue the work in \cite{GL} and study a normalized hypersurface flow in the more general ambient setting of warped product spaces. This flow preserves the volume of the bounded domain enclosed by a graphical hypersurface, and monotonically decreases the hypersurface area. As an application, the isoperimetric problem in warped product spaces is solved for such domains. 
Pengfei Guan, Junfang Li, and Mu-Tao Wang
math.DG math.AP