A zoo of translating solitons on a parallel light-like direction in Minkowski 3-space

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Kocakuşaklı E., Ortega M.

Differential Geometry and its Application, vol.78, 2021 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 78
  • Publication Date: 2021
  • Doi Number: 10.1016/j.difgeo.2021.101796
  • Journal Name: Differential Geometry and its Application
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Keywords: Translating soliton, Mean curvature flow, Light-like vector, Minkowski 3-space, MEAN-CURVATURE FLOW, SURFACES
  • Ankara University Affiliated: Yes

Abstract

© 2021 Elsevier B.V.We deal with solitons of the mean curvature flow. The definition of translating solitons on a light-like direction in Minkowski 3-space is introduced. Firstly, we classify those which are graphical, translation surfaces, obtaining space-like and time-like, entire and not entire, complete and incomplete examples. Among them, all our time-like examples are incomplete. The second family consists of those which are invariant by a 1-dimensional subgroup of parabolic motions, i.e., with light-like axis. The classification result implies that all examples of this second family have singularities.