https://neckpinch.com/authors/francisco-vinado-lereu/New arXiv papers by Francisco Viñado-Lereu, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1908.07441/arxiv:1908.07441Tue, 20 Aug 2019 00:00:00 GMTFrancisco Viñado-Lereu — In the present paper we carry out a systematic study about the flow of a spherical curve by the mean curvature flow with density in a 3-dimensional rotationally symmetric space with density (M³_w, g_w, ξ) where the density ξ decomposes as sum of a radial part φ and an angular part ψ. We analyse how either the parabolicity or the hyperbolicity of (M³_w, g_w) condition the behaviour of the flow when the solution goes to infinity.Mean curvature flowCurve shortening3-manifoldsRotational symmetry & warped products https://neckpinch.com/papers/1607.08402/arxiv:1607.08402Thu, 28 Jul 2016 00:00:00 GMTVicente Miquel, Francisco Viñado-Lereu — We define Type I singularities for the mean curvature flow associated to a density ψ (ψMCF) and describe the blow-up at singular time of these singularities. Special attention is paid to the case where the singularity come from the part of the ψ-curvature due to the density. We describe a family of curves whose evolution under ψMCF (in a Riemannian surface of non-negative curvature with a density which is singular at a geodesic of the surface) produces only type I singularities and study the limits of their blow-ups.Mean curvature flowCurve shorteningSingularities