https://neckpinch.com/authors/vicente-miquel/New arXiv papers by Vicente Miquel, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT 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 https://neckpinch.com/papers/1603.03229/arxiv:1603.03229Thu, 10 Mar 2016 00:00:00 GMTIldefonso Castro, Ana M. Lerma, Vicente Miquel — We describe the evolution under the mean curvature flow of embedded Lagrangian spherical surfaces in the complex Euclidean plane ℂ². In particular, we answer the Question 4.7 addressed in [Ne10b] by A. Neves about finding out a condition on a starting Lagrangian torus in ℂ² such that the corresponding mean curvature flow becomes extinct at finite time and converges after rescaling to the Clifford torus.Mean curvature flowLagrangian mean curvature flowSingularities