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# Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

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1435-5345
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Volume 2019, Issue 746

# A characterization of the grim reaper cylinder

Francisco Martín
• Departamento de Geometría y Topología, Instituto Español de Matemáticas IEMath-GR, Universidad de Granada, 18071, Granada, Spain
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/ Jesús Pérez-García
• Departamento de Geometría y Topología, Instituto Español de Matemáticas IEMath-GR, Universidad de Granada, 18071, Granada, Spain
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/ Andreas Savas-Halilaj
/ Knut Smoczyk
• Institut für Differentialgeometrie & Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
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• De Gruyter OnlineGoogle Scholar
Published Online: 2016-05-21 | DOI: https://doi.org/10.1515/crelle-2016-0011

## Abstract

In this article we prove that a connected and properly embedded translating soliton in ${ℝ}^{3}$ with uniformly bounded genus on compact sets which is ${C}^{1}$-asymptotic to two planes outside a cylinder, either is flat or coincide with the grim reaper cylinder.

## References

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## About the article

Revised: 2015-12-21

Published Online: 2016-05-21

Published in Print: 2019-01-01

Funding Source: MINECO-FEDER

Award identifier / Grant number: MTM2014-52368-P

Award identifier / Grant number: BES-2012-055302

Funding Source: Deutsche Forschungsgemeinschaft

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

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.

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2019, Issue 746, Pages 209–234, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102,

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