Curvature and bubble convergence of harmonic maps

Details Curvature and bubble convergence of harmonic maps Curvature and bubble convergence of harmonic maps

2010-05-20

arxiv.org/abs/1005.3783v3

Mathematics

Differential Geometry

re-worked into a shorter version, inaccuracies and misprints corrected, 17 pages; to appear in J. Geom. Anal

Scientific paper

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.

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