Curvature and bubble convergence of harmonic maps

Gerasim Kokarev

Published 2010-05-20, updated 2011-10-11Version 3

We explore geometric aspects of bubble convergence for harmonic maps. More precisely, we show that the formation of bubbles is characterised by the local excess of curvature on the target manifold. We give a universal estimate for curvature concentration masses at each bubble point and show that there is no curvature loss in the necks. Our principal hypothesis is that the target manifold is Kaehler.