New curvature flows in complex geometry
The Kähler condition is a condition on \((1,1)\)-forms. If one has to implement a condition weaker than it, one faces as obstacle the absence of a \(\partial \bar{\partial}\)-Lemma in non-Kähler geometry. In such a context arises the anomaly flow which is a flow on \((2,2)\)-forms on a \(3\)-dimensional complex manifold and a generalization of the Ricci flow. The paper is a survey of what is known about this and other known curvature flows in non-Kähler geometry and in the theory of non-linear partial differential equations. For the entire collection see [Zbl 1402.14006].
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