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

Authors : Miguel Ortega, Buse Yalçın

Pages : 157-170

Doi:10.36890/iejg.1437356

View : 61 | Download : 71

Publication Date : 2024-04-23

Article Type : Research Paper

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 : Translator, mean curvature flow, hyperbolic Einstein, horospheres, rotationally invariant, hyperbolic space, elliptic PDEs