On a Calabi-type estimate for pluriclosed flow

2019/09/02 by Jordan, Joshua, Streets, Jeffrey · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.00808

Abstract

The regularity theory for pluriclosed flow hinges on obtaining C^α regularity for the metric assuming uniform equivalence to a background metric. This estimate was established in \citeStreetsPCFBI by an adaptation of ideas from Evans-Krylov, the key input being a sharp differential inequality satisfied by the associated `generalized metric' defined on T ⊕ T^*. In this work we give a sharpened form of this estimate with a simplified proof. To begin we show that the generalized metric itself evolves by a natural curvature quantity, which leads quickly to an estimate on the associated Chern connections analogous to, and generalizing, Calabi-Yau's C³ estimate for the complex Monge Ampere equation.

Cited by

• Pluriclosed flow on Oeljeklaus-Toma manifolds
• Almost Calabi-Yau with torsion 6-manifolds and the instanton condition

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