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A characterization of the grim reaper cylinder

  • Francisco Martín EMAIL logo , Jesús Pérez-García , Andreas Savas-Halilaj and Knut Smoczyk


In this article we prove that a connected and properly embedded translating soliton in 3 with uniformly bounded genus on compact sets which is C1-asymptotic to two planes outside a cylinder, either is flat or coincide with the grim reaper cylinder.

Funding source: MINECO-FEDER

Award Identifier / Grant number: MTM2014-52368-P

Award Identifier / Grant number: BES-2012-055302

Award Identifier / Grant number: SM 78/6-1

Funding statement: F. Martín and J. Pérez-García are partially supported by MINECO-FEDER grant no. MTM2014-52368-P. J. Pérez-García is also supported by MINECO (FPI grant, BES-2012-055302) and A. Savas-Halilaj and K. Smoczyk by DFG SM 78/6-1.


The authors would like to thank Brian White and Antonio Ros for many stimulating and helpful conversations. Moreover, the authors would also like to thank Oliver Schnürer and Leonor Ferrer for plenty of useful discussions. Finally, we would like to thank the referee for the valuable comments on the content of the manuscript and the suggestions for improving the paper.


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Received: 2015-08-24
Revised: 2015-12-21
Published Online: 2016-05-21
Published in Print: 2019-01-01

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