Affiliation:
1. Department of Mathematics Columbia University New York New York USA
2. Department of Mathematics Imperial College London London UK
Abstract
AbstractWe prove local Calabi and higher order estimates for solutions to the continuity equation introduced by La Nave–Tian and extended to Hermitian metrics by Sherman–Weinkove. We apply the estimates to show that on a compact complex manifold, the Chern scalar curvature of a solution must blow up at a finite‐time singularity. Additionally, starting from certain classes of initial data on Oeljeklaus–Toma manifolds, we prove Gromov–Hausdorff and smooth convergence of the metric to a particular nonnegative (1,1)‐form as .
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