https://neckpinch.com/authors/miguel-ortega/New arXiv papers by Miguel Ortega, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2403.15166/arxiv:2403.15166Fri, 22 Mar 2024 00:00:00 GMTMiguel Ortega, Buse Yalçın — 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.Mean curvature flowSelf-shrinkers & translatorsStability & uniquenessRotational symmetry & warped products https://neckpinch.com/papers/2211.14529/arxiv:2211.14529Sat, 26 Nov 2022 00:00:00 GMTDiego Artacho, Marie-Amélie Lawn, Miguel Ortega — 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.Mean curvature flowSelf-shrinkers & translatorsPhysics