Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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

Related publications

inJournal
2010 Journal Open Access
Miaomiao Zhu

Harmonic maps from degenerating Riemann surfaces

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