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Transactions of the American Mathematical Society

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


Authors: Pengfei Guan, Junfang Li and Mu-Tao Wang
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 53C23
DOI: https://doi.org/10.1090/tran/7661
Published electronically: May 9, 2019
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Abstract: 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.


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Additional Information

Pengfei Guan
Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 0B9, Canada
Email: guan@math.mcgill.ca

Junfang Li
Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294
Email: jfli@uab.edu

Mu-Tao Wang
Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
Email: mtwang@math.columbia.edu

DOI: https://doi.org/10.1090/tran/7661
Received by editor(s): October 24, 2016
Received by editor(s) in revised form: July 10, 2018
Published electronically: May 9, 2019
Additional Notes: Research of the first author was supported in part by an NSERC Discovery Grant.
This material is based upon work of the third author supported by the National Science Foundation under Grant Number DMS 1405152.
Article copyright: © Copyright 2019 American Mathematical Society