Compactification of moduli space of harmonic mappings

Jingyi Chen, Gang Tian

Research output: Contribution to journalArticle

32 Scopus citations

Abstract

We introduce the notion of harmonic nodal maps from the stratified Riemann surfaces into any compact Riemannian manifolds and prove that the space of the energy minimizing nodal maps is sequentially compact. We also give an existence result for the energy minimizing nodal maps. As an application, we obtain a general existence theorem for minimal surfaces with arbitrary genus in any compact Riemannian manifolds.

Original languageEnglish (US)
Pages (from-to)201-237
Number of pages37
JournalCommentarii Mathematici Helvetici
Volume74
Issue number2
DOIs
StatePublished - Jan 1 1999

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Compactness
  • Harmonic maps
  • Stratified Riemann surface

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