A volume preserving flow and the isoperimetric problem in warped product spaces

By Pengfei Guan, Junfang Li, Mu-Tao Wang. Transactions of the American Mathematical Society, 2016

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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.

Subfields: Applied Mathematics, Computational Mechanics

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