Regularity results for pluriclosed flow

Abstract

In prior work the authors introduced a parabolic flow of pluriclosed metrics. Here we give improved regularity results for solutions to this equation. Furthermore, we exhibit this equation as the gradient flow of the lowest eigenvalue of a certain Schrödinger operator, and show the existence of an expanding entropy functional for this flow. Finally, we motivate a conjectural picture of the optimal regularity results for this flow, and discuss some of the consequences.

Final version, to appear in Geometry and Topology

References in corpus (1)

• Complex Monge-Ampere equations on Hermitian manifolds

Cited by in corpus (8)

• On the evolution of a Hermitian metric by its Chern-Ricci form
• Generalized Kahler Geometry and the Pluriclosed Flow
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• Symplectic curvature flow
• Kähler Uniformization from Holographic Renormalization Group Flows of M5-branes
• Generalized geometry, T-duality, and renormalization group flow
• Special Hermitian metrics and Lie groups
• Static SKT metrics on Lie groups