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We consider the energy-critical Schroedinger map initial value problem withsmooth initial data from R^2 into the sphere S^2. Given sufficientlyenergy-dispersed data with subthreshold energy, we prove that the system admitsa unique global smooth solution. This improves earlier analogous conditionalresults. The key behind this improvement lies in exploiting estimates on thecommutator of the Schroedinger map and harmonic map heat flows.

Global regularity of critical Schr\"odinger maps: subthreshold dispersed energy