The mean curvature flow on solvmanifolds

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 their geometry that are relevant to our work. We finish by posing the equations that describe translating solutions to mean curvature flow on a 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.