Gradient estimates and blow-up analysis for stationary harmonic maps

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)785-829
Number of pages45
JournalAnnals of Mathematics
Volume149
Issue number3
StatePublished - May 1999

Fingerprint

Blow-up Analysis
Gradient Estimate
Harmonic Maps
Singular Set
Energy
Riemannian Manifold
Interior
Defects
Harmonic
Necessary Conditions
Target
Sufficient Conditions
Blow-up
Gradient

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Annals of Mathematics, Vol. 149, No. 3, 05.1999, p. 785-829.

Research output: Contribution to journalArticle

@article{5de23d328cb64abf9603bec9e76f0c6c,
title = "Gradient estimates and blow-up analysis for stationary harmonic maps",
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.",
author = "Fang-Hua Lin",
year = "1999",
month = "5",
language = "English (US)",
volume = "149",
pages = "785--829",
journal = "Annals of Mathematics",
issn = "0003-486X",
publisher = "Princeton University Press",
number = "3",

}

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

AN - SCOPUS:0033470202

VL - 149

SP - 785

EP - 829

JO - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

IS - 3

ER -