https://neckpinch.com/authors/giuseppe-pipoli/New arXiv papers by Giuseppe Pipoli, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2211.03918/arxiv:2211.03918Tue, 08 Nov 2022 00:00:00 GMTRonaldo F. de Lima, Giuseppe Pipoli — We consider translators to the extrinsic flows in ℝⁿ×ℝ and ℍⁿ×ℝ (called r-mean curvature flows or r-MCF, for short) whose velocity functions are the higher order mean curvatures Hᵣ. We show that there exist rotational bowl-type and catenoid-type translators to r-MCF in both ℝⁿ×ℝ and ℍⁿ×ℝ, and also that there exist parabolic and hyperbolic catenoid-type translators to r-MCF in ℍⁿ×ℝ. In addition, we show that there exist Grim Reaper-type translators to Gaussian flow (n-MCF) in ℝⁿ×ℝ and ℍⁿ×ℝ. We also establish the uniqueness of all these translators (together with certain cylinders) among those which are invariant by either rotations or translations (Euclidean, parabolic or hyperbolic). We apply this uniqueness result to classify the translators to r-MCF in ℝⁿ×ℝ and ℍⁿ×ℝ whose r-th mean curvature is constant, as well as those which are isoparametric. Our results extend to the context of r-MCF in ℝⁿ×ℝ and ℍⁿ×ℝ the existence and uniqueness theorems by Altschuler–Wu (of the bowl soliton) and Clutterbuck–Schnürer–Schulze (of the translating catenoids) in Euclidean space.Mean curvature flowSelf-shrinkers & translatorsStability & uniqueness