https://neckpinch.com/authors/raquel-perales/New arXiv papers by Raquel Perales, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2311.01342/arxiv:2311.01342Thu, 02 Nov 2023 00:00:00 GMTShouhei Honda, Christian Ketterer, Ilaria Mondello, Raquel Perales, Chiara Rigoni — We establish a nonlinear analogue of a splitting map into a Euclidean space, as a harmonic map into a flat torus. We prove that the existence of such a map implies Gromov-Hausdorff closeness to a flat torus in any dimension. Furthermore, Gromov-Hausdorff closeness to a flat torus and an integral bound on r_M(x), the smallest eigenvalue of the Ricci tensor ricₓ in x, imply the existence of a harmonic splitting map. Combining these results with Stern's inequality, we provide a new Gromov-Hausdorff stability theorem for flat 3-tori. The main tools we employ include the harmonic map heat flow, Ricci flow, and both Ricci limits and RCD theories.Ricci flowScalar curvatureLimit spaces & RCDStability & uniquenessHarmonic maps & DeTurck trickEigenvalues & spectrum 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