Laplacian flow for closed G_2 structures: real analyticity

Abstract

Let $\phi (t),t\in [0,T]$ be a smooth solution to the Laplacian flow for closed G_2 structures on a compact 7-manifold $M$. We show that for each fixed positive time $t\in (0,T]$, $(M,\phi (t),g(t))$ is real analytic, where $g(t)$ is the metric induced by $\phi (t)$. Consequently, any Laplacian soliton is real analytic and we obtain unique continuation results for the flow.

27 pages, v2: streamlined exposition, accepted version for CAG

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