https://neckpinch.com/authors/jorge-herbert-soares-de-lira/New arXiv papers by Jorge Herbert Soares de Lira, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2604.18974arxiv:2604.18974Tue, 21 Apr 2026 00:00:00 GMTJorge Herbert Soares de Lira, Rafael Rocha de Farias — In this paper we prove existence and classification results for translating solitons defined as initial conditions for higher order mean curvature flows that are invariant by translations in warped product manifolds ℙ×_χℝ. Here, ℙ is a Cartan-Hadamard manifold endowed with a rotationally symmetric metric and χ is a radial function defined in ℙ. In this setting, the higher order mean curvature flow is, up to a change of time parameter, given by translations along the factor ℝ in the warped product. This setting encompasses the cases of translating solitons in ℝⁿ⁺¹, ℍⁿ × ℝ and ℍⁿ⁺¹ studied in recent papers. In particular we prove the existence of families of bowl-type and catenoid-type translating solitons under mild assumptions about the curvature of the warped product. We also describe the asymptotic behavior for those solitons in terms of the geometry at infinity of ℙ. Our assumptions about the ambient metric allow us to control the higher order mean curvature of cylinders and to use them as barriers.Mean curvature flowSelf-shrinkers & translatorsRotational symmetry & warped products https://arxiv.org/abs/2603.12548arxiv:2603.12548Fri, 13 Mar 2026 00:00:00 GMTClaudia Fernandes, Jorge de Lira, Matheus Soares — A priori estimates for the mean curvature evolution of Killing graphs in Cartan-Hadamard manifolds with asymptotic Dirichlet conditions are established. As an application, the existence of the corresponding parabolic flow is proved, ensuring regularity of the obtained solutions through the construction of suitable barriers at points of the asymptotic boundary. Such a construction is made possible under an appropriate notion of convexity at infinity.Mean curvature flow https://arxiv.org/abs/2602.11930arxiv:2602.11930Thu, 12 Feb 2026 00:00:00 GMTJocel Faustino Norberto de Oliveira, Jorge Herbert Soares de Lira, Matheus Nunes Soares — We obtain height, gradient, and curvature a priori estimates for a modified mean curvature flow in Riemannian manifolds endowed with a Killing vector field. As a consequence, we prove the existence of smooth, entire, longtime solutions for this extrinsic flow with smooth initial data.Mean curvature flowLong-time existence & convergence https://arxiv.org/abs/2202.04158arxiv:2202.04158Tue, 08 Feb 2022 00:00:00 GMTJorge Lira, Fernanda Roing — We prove the longtime existence for the mean curvature flow problem with a perpendicular Neumann boundary condition in a Generalized Robertson Walker (GRW) spacetime that obeys the null convergence condition. In addition, we prove that the metric of such a solution is conformal to the one of the leaf of the GRW in asymptotic time. Furthermore, if the initial hypersurface is mean convex, then the evolving hypersurfaces remain mean convex during the flow.Mean curvature flowBoundaries & non-compactFree boundary & capillaryLong-time existence & convergence