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Transactions of the American Mathematical Society

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

 
 

 

The perpendicular Neumann problem for mean curvature flow with a timelike cone boundary condition


Author: Ben Lambert
Journal: Trans. Amer. Math. Soc. 366 (2014), 3373-3388
MSC (2010): Primary 53C44, 35K59
DOI: https://doi.org/10.1090/S0002-9947-2014-05865-0
Published electronically: March 20, 2014
MathSciNet review: 3192599
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Abstract: This paper demonstrates existence for all time of mean curvature flow in Minkowski space with a perpendicular Neumann boundary condition, where the boundary manifold is a convex cone and the flowing manifold is initially spacelike. Using a blowdown argument, we show that under renormalisation this flow converges towards a homothetically expanding hyperbolic solution.


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Additional Information

Ben Lambert
Affiliation: Department of Mathematics, University of Konstanz, Zukunftskolleg, Box 216, 78457 Konstanz, Germany
Email: benjamin.lambert@uni-konstanz.de

DOI: https://doi.org/10.1090/S0002-9947-2014-05865-0
Received by editor(s): December 8, 2011
Published electronically: March 20, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.