On the pluriclosed flow on Oeljeklaus-Toma manifolds

We investigate the pluriclosed flow on Oeljeklaus-Toma manifolds. We parametrize left-invariant pluriclosed metrics on Oeljeklaus-Toma manifolds and we classify the ones which lift to an algebraic soliton of the pluriclosed flow on the universal covering. We further show that the pluriclosed flow starting from a left-invariant pluriclosed metric has a long-time solution $ω_t$ which once normalized collapses to a torus in the Gromov-Hausdorff sense. Moreover the lift of $\tfrac{1}{1+t}ω_t$ to the universal covering of the manifold converges in the Cheeger-Gromov sense to $(\mathbb H^r\times\mathbb C^s, \tildeω_{\infty})$ where $\tildeω_{\infty}$ is an algebraic soliton.

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