Laplacian Flow on Complete Non-Compact 7-Manifolds

This project establishes short-time existence and uniqueness for the Laplacian flow of G2-Structures in the complete non-compact setting under the assumption of bounded curvature and torsion (in the sense of Lotay-Wei). The procedure for establishing these results parallels Shi's work for the Ricci flow. Namely, I first look at the Laplacian-deTurck flow as a boundary problem, then use C0 estimates to show a solution exists on the entire non-compact manifold by exhausting the space with such domains, and then use these estimates to relate the global solution to the Laplacian-deTurck flow to a genuine Laplacian flow solution. I later intend to apply this result to specific non-compact G2-Structures, namely in terms of understanding stability of the Bryant-Salamon manifolds. 

Forthcoming. Submitted manuscript will be available here.