Flows of co-closed $G_{2}$-structures

Sergey Grigorian

paper

Flows of co-closed $G_{2}$ -structures

arXiv:1811.10505

Abstract

We survey recent progress in the study of $G_{2}$ -structure Laplacian coflows, that is, heat flows of co-closed $G_{2}$ -structures. We introduce the properties of the original Laplacian coflow of $G_{2}$ -structures as well as the modified coflow, reviewing short-time existence and uniqueness results for the modified coflow and well as recent Shi-type estimates that apply to a more general class of $G_{2}$ -structure flows.

To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics"

Flows of co-closed G2​-structures

Abstract

Flows of co-closed $G_{2}$ -structures