https://neckpinch.com/authors/irene-ortiz/New arXiv papers by Irene Ortiz, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2402.07237/arxiv: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://neckpinch.com/papers/2201.07480/arxiv: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