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

Pengfei Guan McGill University Junfang Li University of Alabama Mu-Tao Wang Columbia University

Analysis of PDEs Differential Geometry Geometric Analysis and Geometric Topology Metric Geometry mathscidoc:1804.03009

In this article, we continue the work in Guan-Li 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.
isoperimetric problem, geometric flows
[ Download ] [ 2018-04-30 14:24:26 uploaded by mutaowang ] [ 1539 downloads ] [ 0 comments ]
  • arXiv:1609.08238
@inproceedings{pengfeia,
  title={A volume preserving flow and the isoperimetric problem in warped product spaces},
  author={Pengfei Guan, Junfang Li, and Mu-Tao Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180430142427027617080},
}
Pengfei Guan, Junfang Li, and Mu-Tao Wang. A volume preserving flow and the isoperimetric problem in warped product spaces. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180430142427027617080.
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