https://neckpinch.com/authors/rafael-belli/New arXiv papers by Rafael Belli, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2607.00943/arxiv:2607.00943Wed, 01 Jul 2026 00:00:00 GMTRafael Belli, Rafael López — In this paper, we classify all solitons of the Gauss curvature flow in the three-dimensional Heisenberg group Nil₃ that are invariant under a one-parameter group of ambient isometries. By means of the four canonical types of Killing vector fields and the three families of invariant surfaces (vertical translations, horizontal translations, and helicoidal motions), we analyze the twelve resulting types of possible solitons. In some cases, there do not exist any invariant solitons; in others, we find explicit parametrizations, or describe their geometric properties.Other curvature flowsGauss curvature flow3-manifolds https://neckpinch.com/papers/2605.17097/arxiv:2605.17097Sat, 16 May 2026 00:00:00 GMTRafael Belli, Rafael López — We classify invariant surfaces in the 3-dimensional solvable Lie group sol that act as solitons for the Gauss curvature flow. We consider solitons associated with the canonical basis of Killing vector fields F₁, F₂, F₃\, where F₁ and F₂ generate horizontal translations and F₃ generates the scaling isometry. We establish rigidity results for F₃-invariant surfaces, proving that specific totally geodesic vertical planes are the only F₁- and F₂-solitons. For F₁-invariant surfaces, we establish the main geometric properties of F₂- and F₃-solitons in both the extrinsic and intrinsic Gauss curvature.Other curvature flowsGauss curvature flow3-manifoldsHomogeneous spacesStability & uniqueness