A VOLUME PRESERVING FLOW AND THE ISOPERIMETRIC PROBLEM IN WARPED PRODUCT SPACES

摘要

In this article, we continue the work in [Int. Math. Res. Not. IMRN 13 (2015), pp. 4716-4740] 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.