Harmonic maps from degenerating Riemann surfaces
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Submission date: 25. Mar. 2008
published in: Mathematische Zeitschrift, 264 (2010) 1, p. 63-85
DOI number (of the published article): 10.1007/s00209-008-0452-0
Keywords and phrases: harmonic maps, compactness, generalized energy identity
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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 and modulo bubbles of sequences of such maps.