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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Mean curvature flow of compact spacelike submanifolds in higher codimension


Authors: Brendan Guilfoyle and Wilhelm Klingenberg
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 35K40; Secondary 53A35
DOI: https://doi.org/10.1090/tran/7766
Published electronically: February 1, 2019
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Abstract: We prove the longtime existence for mean curvature flow of a smooth $ n$-dimensional spacelike submanifold of an ($ n+m$)-dimensional manifold whose metric satisfies the timelike curvature condition.


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Additional Information

Brendan Guilfoyle
Affiliation: School of Science, Technology, Engineering and Mathematics, Institute of Technology, Tralee, Clash, Tralee, County Kerry, Ireland
Email: brendan.guilfoyle@ittralee.ie

Wilhelm Klingenberg
Affiliation: Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom
Email: wilhelm.klingenberg@durham.ac.uk

DOI: https://doi.org/10.1090/tran/7766
Received by editor(s): August 7, 2016
Received by editor(s) in revised form: October 2, 2017, and November 21, 2018
Published electronically: February 1, 2019
Article copyright: © Copyright 2019 American Mathematical Society