Nonstationary weak limit of a stationary harmonic map sequence

Let M and N be two compact Riemannian manifolds. Let uk be a sequence of stationary harmonic maps from M to N with bounded energies. We may assume that it converges weakly to a weakly harmonic map u in H1,2 (M, N) as k → ∞. In this paper, we construct an example to show that the limit map u may not...

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Bibliographic Details
Published inCommunications on pure and applied mathematics Vol. 56; no. 2; pp. 270 - 277
Main Authors Ding, Weiyue, Li, Jiayu, Li, Wei
Format Journal Article
LanguageEnglish
Published New York Wiley Subscription Services, Inc., A Wiley Company 01.02.2003
Wiley
Subjects
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematics
Ordinary differential equations
Sciences and techniques of general use
Hausdorff dimension
Stationary sequence
Riemann manifold
Sequence(mathematics)
Harmonic analysis
Harmonic map
Compact manifold
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Summary:Let M and N be two compact Riemannian manifolds. Let uk be a sequence of stationary harmonic maps from M to N with bounded energies. We may assume that it converges weakly to a weakly harmonic map u in H1,2 (M, N) as k → ∞. In this paper, we construct an example to show that the limit map u may not be stationary. © 2002 Wiley Periodicals, Inc.
Bibliography:ark:/67375/WNG-C50Q377D-R
National Key Basic Research Fund of China
istex:FC57CAE13121A34E22D73F1ACE2AD9460B2E0890
ArticleID:CPA10058
National Science Foundation of China
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.10058