https://neckpinch.com/authors/pedro-gaspar/New arXiv papers by Pedro Gaspar, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2507.03837/arxiv:2507.03837Fri, 04 Jul 2025 00:00:00 GMTJingwen Chen, Pedro Gaspar — From the perspective of Morse theory, it is natural to investigate gradient flow trajectories between critical points. In this short note, we explore the minimal hypersurface analogue of this phenomenon and present examples that suggest additional topological and variational obstructions to the existence of connecting mean curvature flows.Mean curvature flowMinimal & CMC surfaces https://neckpinch.com/papers/2107.09140/arxiv:2107.09140Mon, 19 Jul 2021 00:00:00 GMTJingwen Chen, Pedro Gaspar — In this article we study eternal solutions to the Allen-Cahn equation in the 3-sphere, in view of the connection between the gradient flow of the associated energy functional, and the mean curvature flow. We construct eternal integral Brakke flows that connect Clifford tori to equatorial spheres, and study a family of such flows, in particular their symmetry properties. Our approach is based on the realization of Brakke's motion by mean curvature as a singular limit of Allen-Cahn gradient flows, as studied by Ilmanen, and Tonegawa, and it uses the classification of ancient gradient flows in spheres, by K. Choi and C. Mantoulidis, as well as the rigidity of stationary solutions with low Morse index proved by F. Hiesmayr.Mean curvature flowAncient solutionsWeak & singular flowsStability & uniquenessPhase fields & multiphase flows