Laplacian flow for closed $\mathrm{G}_2$ structures: real analyticity

Let $\varphi (t), t \in [0, T_0]$ be a solution to the Laplacian flow for closed $G2$ structures on a compact $7$-manifold $M$. We show that for each fixed time $t \in (0, T_0], (M,\varphi (t), g(t))$ is real analytic, where $g(t)$ is the metric induced by $\varphi (t)$. Consequently, any Laplacian soliton is real analytic and we obtain unique continuation results for the flow.

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This research was supported by EPSRC grant EP/K010980/1.

Received 23 January 2016

Published 7 May 2019