We show that immersed Lagrangian Floer cohomology in compact rational symplectic manifolds is invariant under Maslov flow; this includes coupled mean curvature/Kähler–Ricci flow in the sense of Smoczyk (Leipzig University, 2001). In particular, we show invariance when a pair of self-intersection points is born or dies at a self-tangency, using results of Ekholm, Etnyre and Sullivan (J. Differential Geom. 71 (2005) 177–305). Using this we prove a lower bound on the time for which the immersed Floer theory is invariant under the flow, if it exists. This proves part of a conjecture of Joyce (EMS Surv. Math. Sci. 2 (2015) 1–62).
Joseph Palmer. Chris Woodward. "Invariance of immersed Floer cohomology under Maslov flows." Algebr. Geom. Topol. 21 (5) 2313 - 2410, 2021. https://doi.org/10.2140/agt.2021.21.2313