https://neckpinch.com/authors/antonio-bueno/New arXiv papers by Antonio Bueno, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2606.31641arxiv:2606.31641Tue, 30 Jun 2026 00:00:00 GMTAntonio Bueno — We study oriented surfaces in the Heisenberg space Nil₃ whose mean curvature H at each point is H=⟨ N,∂_z⟩+λ, where N is the unit normal, ∂_z is the vertical Killing vector field and λ∈ℝ. These surfaces are known as λ-translators and generalize, among others, minimal and positive constant mean curvature surfaces, and also translating solitons of the mean curvature flow. The objective in this paper is to classify λ-translators invariant by the following one-parameter groups of isometries of Nil₃: left-translations, rotations and helicoidal motions.Mean curvature flowSelf-shrinkers & translatorsMinimal & CMC surfaces https://arxiv.org/abs/2402.07237arxiv:2402.07237Sun, 11 Feb 2024 00:00:00 GMTAntonio Bueno, Irene Ortiz — Given λ∈ℝ and v∈L³, a λ-translator with velocity v is an immersed surface in L³ whose mean curvature satisfies H=⟨ N,v⟩+λ, where N is a unit normal vector field. When λ=0, we fall into the class of translating solitons of the mean curvature flow. In this paper we study λ-translators in L³ that are invariant under a 1-parameter group of translations and rotations. The former are cylindrical surfaces and explicit parametrizations are found, distinguishing on the causality of both the ruling direction and the λ-translators. In the case of rotational λ-translators we distinguish between spacelike and timelike rotations and exhibit the qualitative properties of rotational λ-translators by analyzing the non-linear autonomous system fulfilled by the coordinate functions of the generating curves.Mean curvature flowSelf-shrinkers & translatorsPhysics https://arxiv.org/abs/2402.05772arxiv:2402.05772Thu, 08 Feb 2024 00:00:00 GMTAntonio Bueno, Rafael López — We study translators of the mean curvature flow in the product space h²×r. In h²×r there are three types of translations: vertical translations due to the factor r and parabolic and hyperbolic translations from h². A grim reaper in h²×r is a translator invariant by a one-parameter group of translations. The variety of translators and translations in h²×r makes that the family of grim reapers particularly rich. In this paper we give a full classification of the grim reapers of h²×r with a description of their geometric properties. In some cases, we obtain explicit parametrizations of the surfaces.Mean curvature flowSelf-shrinkers & translators https://arxiv.org/abs/2201.07480arxiv:2201.07480Wed, 19 Jan 2022 00:00:00 GMTAntonio Bueno, Irene Ortiz — Given a,b∈ℝ and Φ∈ C¹(S²), we study immersed oriented surfaces Σ in the Euclidean 3-space ℝ³ whose mean curvature H and Gauss curvature K satisfy 2aH+bK=Φ(N), where N:Σ→S² is the Gauss map. This theory widely generalize some of paramount importance such as the ones constant mean and Gauss curvature surfaces, linear Weingarten surfaces and self-translating solitons of the mean curvature flow. Under mild assumptions on the prescribed function Φ, we exhibit a classification result for rotational surfaces in the case that the underlying fully nonlinear PDE that governs these surfaces is elliptic or hyperbolic.Mean curvature flowSelf-shrinkers & translators