https://neckpinch.com/authors/romina-m-arroyo/New arXiv papers by Romina M. Arroyo, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2505.17892/arxiv:2505.17892Fri, 23 May 2025 00:00:00 GMTRomina M. Arroyo, Gabriela P. Ovando, Mariel Sáez — In this work we study the existence of solutions to the Mean Curvature Flow for which the initial condition has the structure of a two-dimensional Lie subgroup within a Lie group of dimension three. We consider Lie groups with a fixed left-invariant metric and first observe that if the Lie group is unimodular, then every Lie subgroup is a minimal surface (hence a trivial solution). For this reason we focus on non-unimodular Lie groups, finding the evolution of every Lie subgroup of dimension 2 (within a 3 dimensional Lie group). These evolutions are self-similar for abelian subgroups (i.e. evolve by isometries), but not self-similar in the other cases.Mean curvature flow3-manifoldsSurfacesHomogeneous spacesMinimal & CMC surfaces https://neckpinch.com/papers/2305.02378/arxiv:2305.02378Wed, 03 May 2023 00:00:00 GMTRomina M. Arroyo, Gabriela P. Ovando, Raquel Perales, Mariel Sáez — This work is a survey of the most relevant background material to motivate and understand the construction and classification of translating solutions to mean curvature flow on a family of solvmanifolds. We introduce the mean curvature flow and some known results in the field. In particular we explore the notion of translating solution in the Euclidean space and extensions into other Riemannian manifolds. We also include a discussion on solvmanifolds and some elements of its geometry that are relevant to our work. We finish by posing the equations that describe translating solutions to mean curvature flow on our family of 3-dimensional solvmanifolds with some additional assumptions. This project emerged at the "Latin American and Caribbean Workshop on Mathematics and Gender" held at Casa Matemática Oaxaca (CMO) from May 15-20, 2022.Mean curvature flowSelf-shrinkers & translators3-manifoldsHomogeneous spaces