The Anomaly flow and the Fu-Yau equation

Abstract

The Anomaly flow is shown to converge on toric fibrations with the Fu-Yau ansatz, for both positive and negative values of the slope parameter ${\alpha }^{\prime }$. This implies both results of Fu and Yau on the existence of solutions for Hull-Strominger systems, which they proved using different methods depending on the sign of ${\alpha }^{\prime }$. It is also the first case where the Anomaly flow can even be shown to exist for all time. This is in itself remarkable from the point of view of the theory of fully nonlinear partial differential equations, as the elliptic terms in the flow are not concave.

54 pages; details added

References in corpus (1)

• The parabolic Monge-Ampère equation on compact almost Hermitian manifolds

Cited by in corpus (6)

• Fu-Yau Hessian Equations
• Regularizing properties of Complex Monge-Ampère flows II: Hermitian manifolds
• New curvature flows in complex geometry
• A flow of conformally balanced metrics with Kähler fixed points
• The Anomaly flow on unimodular Lie groups
• Parabolic complex Monge-Ampère equations on compact Hermitian manifolds