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. 372 (2019), 2777-2798
MSC (2010):
Primary 53C23
DOI:
https://doi.org/10.1090/tran/7661
Published electronically:
May 9, 2019
MathSciNet review:
3988593
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Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
772604
Email:
jfli@uab.edu
Mu-Tao Wang
Affiliation:
Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
MR Author ID:
626881
Email:
mtwang@math.columbia.edu
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