Pluriclosed flow on Oeljeklaus-Toma manifolds

TL;DR

This paper proves the global existence of pluriclosed flow on Oeljeklaus-Toma manifolds and explores convergence properties, providing new insights into complex geometric flows on these non-Kähler manifolds.

Contribution

It establishes the first global existence results for pluriclosed flow on Oeljeklaus-Toma manifolds and analyzes convergence to tori under certain bounds.

Findings

Global existence of pluriclosed flow on Oeljeklaus-Toma manifolds

Gromov-Hausdorff convergence of blowdown limits to a torus

Refined a priori estimates for generalized Kähler-Ricci flow

Abstract

We establish global existence of the pluriclosed flow with arbitrary initial data on Oeljeklaus-Toma manifolds, and Gromov-Hausdorff convergence of blowdown limits to a torus under natural conjectural bounds on the flow at infinity. In the case of generalized K\"ahler-Ricci flow we prove refined a priori estimates in support of these conjectural bounds.