The Anomaly flow over Riemann surfaces

Abstract

We initiate the study of a new nonlinear parabolic equation on a Riemann surface. The evolution equation arises as a reduction of the Anomaly flow on a fibration. We obtain a criterion for long-time existence for this flow, and give a range of initial data where a singularity forms in finite time, as well as a range of initial data where the solution exists for all time. A geometric interpretation of these results is given in terms of the Anomaly flow on a Calabi-Yau threefold.

22 pages

References in corpus (2)

• The Kähler-Ricci flow on surfaces of positive Kodaira dimension
• Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton

Cited by in corpus (7)

• Fu-Yau Hessian Equations
• Geometric Partial Differential Equations from Unified String Theories
• The Hull-Strominger system and the Anomaly flow on a class of solvmanifolds
• New curvature flows in complex geometry
• Parabolic Dimensional Reductions of 11D Supergravity
• A flow of conformally balanced metrics with Kähler fixed points
• The Anomaly flow on nilmanifolds