Paper · Nov 26, 2022
New Examples of Translating Solitons in Generalised Robertson-Walker Geometries
As on arXiv
Abstract
Translators can be regarded as submanifolds which satisfy the mean curvature flow equation when evolving by translations along a distinguished vector field of the ambient space. We study translators in Generalised Robertson-Walker spacetimes, due to their importance as Lorentzian manifolds, and because they admit a natural conformal Killing timelike vector field carrying substantial geometric information, which will play the role of this translating vector field. We identify three one-parameter families of warping functions for which these objects exist. As a first example of this notion of translator, we classify the analogues of the classical Grim Reapers within this context.
- Submitted
- Nov 26, 2022
- Last revised
- Sep 29, 2025 (v2)
- Subjects
- math.DG
- Journal
- Asian J. Math. vol 29 (2025), pp. 711-732
Comments: 27 pages. To appear in the Asian Journal of Mathematics
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Background reading
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In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.