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MiS Preprint
24/2008

Harmonic maps from degenerating Riemann surfaces

Miaomiao Zhu

Abstract

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.

Received:
Mar 25, 2008
Published:
Mar 25, 2008
MSC Codes:
58E20
Keywords:
harmonic maps, compactness, generalized energy identity

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Miaomiao Zhu

Harmonic maps from degenerating Riemann surfaces

In: Mathematische Zeitschrift, 264 (2010) 1, pp. 63-85