English

Translators of the Mean Curvature Flow in Hyperbolic Einstein's Static Universe

Differential Geometry 2024-04-16 v1

Abstract

In this study, we deal with non-degenerate translators of the mean curvature flow in the well-known hyperbolic Einstein's static universe. We classify translators foliated by horospheres and rotationally invariant ones, both space-like and time-like. For space-like translators, we show a uniqueness theorem as well as a result to extend an isometry of the boundary of the domain to the whole translator, under simple conditions. As an application, we obtain a characterization of the the bowl when the boundary is a ball, and of certain translators foliated by horospheres whose boundary is a rectangle.

Keywords

Cite

@article{arxiv.2403.15166,
  title  = {Translators of the Mean Curvature Flow in Hyperbolic Einstein's Static Universe},
  author = {Miguel Ortega and Buse Yalçın},
  journal= {arXiv preprint arXiv:2403.15166},
  year   = {2024}
}