Harmonic maps from degenerating Riemann surfaces

Details Harmonic maps from degenerating Riemann surfaces Harmonic maps from degenerating Riemann surfaces

2008-03-25

arxiv.org/abs/0803.3575v1

Math. Z. 264 (2010), no. 1, 63-85

Mathematics

Differential Geometry

27 pages

Scientific paper

We study harmonic maps from degenerating Riemann surfaces with uniformly
bounded energy and show the so-called generalized energy identity. We find
conditions that are both necessary and sufficient for the compactness in
$W^{1,2}$ and $C^{0}$ modulo bubbles of sequences of such maps.

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