Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

Online
ISSN
1435-5345
See all formats and pricing
More options …
Volume 2019, Issue 746

Issues

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
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Jesús Pérez-García
  • Departamento de Geometría y Topología, Instituto Español de Matemáticas IEMath-GR, Universidad de Granada, 18071, Granada, Spain
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Andreas Savas-Halilaj / Knut Smoczyk
  • Institut für Differentialgeometrie & Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
  • Email
  • Other articles by this author:
  • 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 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.

References

  • [1]

    A. D. Alexandrov, Uniqueness theorems for surfaces in the large, Vestnik Leningrad Univ. Math. 11 (1956), 5–17. Google Scholar

  • [2]

    H. I. Choi and R. Schoen, The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature, Invent. Math. 81 (1985), 387–394. CrossrefGoogle Scholar

  • [3]

    J. Dávila, M. del Pino and X.-H. Nguyen, Finite topology self-translating surfaces for the mean curvature flow in 3, preprint (2015), http://arxiv.org/abs/1501.03867.

  • [4]

    T. Ilmanen, Elliptic regularization and partial regularity for motion by mean curvature, Mem. Amer. Math. Soc. 108 (1994), no. 520. Google Scholar

  • [5]

    F. Martín, A. Savas-Halilaj and K. Smoczyk, On the topology of translating solitons of the mean curvature flow, Calc. Var. Partial Differential Equations 54 (2015), 2853–2882. Web of ScienceCrossrefGoogle Scholar

  • [6]

    X.-H. Nguyen, Translating tridents, Comm. Partial Differential Equations 34 (2009), 257–280. CrossrefGoogle Scholar

  • [7]

    X.-H. Nguyen, Complete embedded self-translating surfaces under mean curvature flow, J. Geom. Anal. 23 (2013), 1379–1426. Web of ScienceCrossrefGoogle Scholar

  • [8]

    X.-H. Nguyen, Doubly periodic self-translating surfaces for the mean curvature flow, Geom. Dedicata 174 (2015), 177–185. CrossrefGoogle Scholar

  • [9]

    J. Pérez and A. Ros, Properly embedded minimal surfaces with finite total curvature, The global theory of minimal surfaces in flat spaces (Martina Franca 1999), Lecture Notes in Math. 1775, Springer, Berlin (2002), 15–66. Google Scholar

  • [10]

    R. M. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, J. Differential Geom. 18 (1983), 791–809. CrossrefGoogle Scholar

  • [11]

    G. Smith, On complete embedded translating solitons of the mean curvature flow that are of finite genus, preprint (2015), http://arxiv.org/abs/1501.04149.

  • [12]

    B. White, Evolution of curves and surfaces by mean curvature, Proceedings of the international congress of mathematicians – ICM 2002. Vol. I: Plenary lectures and ceremonies (Beijing 2002), Higher Education Press, Beijing (2002), 525–538. Google Scholar

  • [13]

    B. White, On the compactness theorem for embedded minimal surfaces in 3-manifolds with locally bounded area and genus, preprint (2015), http://arxiv.org/abs/1503.02190v1.

  • [14]

    B. White, Controlling area blow-up in minimal or bounded mean curvature varieties, J. Differential Geom. 102 (2016), no. 3, 501–535. CrossrefGoogle Scholar

About the article

Received: 2015-08-24

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, DOI: https://doi.org/10.1515/crelle-2016-0011.

Export Citation

© 2018 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Luis J. Alías, Jorge H. de Lira, and Marco Rigoli
The Journal of Geometric Analysis, 2019

Comments (0)

Please log in or register to comment.
Log in