Gradient estimates and blow-up analysis for stationary harmonic maps

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For stationary harmonic maps between Riemannian manifolds, we provide a necessary and sufficient condition for the uniform interior and boundary gradient estimates in terms of the total energy of maps. We also show that if analytic target manifolds do not carry any harmonic double-struck S sign2, then the singular sets of stationary maps are m ≤ n - 4 rectifiable. Both of these results follow from a general analysis on the defect measures and energy concentration sets associated with a weakly converging sequence of stationary harmonic maps.

Original languageEnglish (US)
Pages (from-to)785-829
Number of pages45
JournalAnnals of Mathematics
Issue number3
StatePublished - May 1999

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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