Laplacian Flow for Closed $G_2$-Structures: Short Time Behavior

TL;DR

This paper establishes the short time existence and uniqueness of solutions to the Laplacian flow for closed G2-structures on compact 7-manifolds, filling a gap in the mathematical literature.

Contribution

It provides the first rigorous proof of short time existence and uniqueness for the Laplacian flow of closed G2-structures, previously claimed but not proven.

Findings

Proves short time existence of solutions

Establishes uniqueness of solutions

Fills a gap in mathematical literature on G2-structures

Abstract

We prove short time existence and uniqueness of solutions to the Laplacian flow for closed $G_2$ structures on a compact manifold $M^7$. The result was claimed in \cite{BryantG2}, but its proof has never appeared.