### Abstract

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 sign
^{2}, 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 language | English (US) |
---|---|

Pages (from-to) | 785-829 |

Number of pages | 45 |

Journal | Annals of Mathematics |

Volume | 149 |

Issue number | 3 |

State | Published - May 1999 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Annals of Mathematics*,

*149*(3), 785-829.

**Gradient estimates and blow-up analysis for stationary harmonic maps.** / Lin, Fang-Hua.

Research output: Contribution to journal › Article

*Annals of Mathematics*, vol. 149, no. 3, pp. 785-829.

}

TY - JOUR

T1 - Gradient estimates and blow-up analysis for stationary harmonic maps

AU - Lin, Fang-Hua

PY - 1999/5

Y1 - 1999/5

N2 - 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 sign 2, 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.

AB - 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 sign 2, 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.

UR - http://www.scopus.com/inward/record.url?scp=0033470202&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033470202&partnerID=8YFLogxK

M3 - Article

VL - 149

SP - 785

EP - 829

JO - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

IS - 3

ER -