Bubble tree convergence for harmonic maps

@article{Parker1996BubbleTC,
  title={Bubble tree convergence for harmonic maps},
  author={Thomas H. Parker},
  journal={Journal of Differential Geometry},
  year={1996},
  volume={44},
  pages={595-633}
}
Let Σ be a compact Riemann surface. Any sequence fn : Σ — > M of harmonic maps with bounded energy has a "bubble tree limit" consisting of a harmonic map /o : Σ -> M and a tree of bubbles fk : S2 -> M. We give a precise construction of this bubble tree and show that the limit preserves energy and homotopy class, and that the images of the fn converge pointwise. We then give explicit counterexamples showing that bubble tree convergence fails (i) for harmonic maps fn when the conformal structure… Expand

Figures from this paper

Bubble tree convergence for the harmonic sequence of harmonic surfaces in ℂℙn
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Compactness of harmonic maps of surfaces with regular nodes
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Bubble tree for approximate harmonic maps
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