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BUBBLING LOCATION FOR SEQUENCES OF APPROXIMATE f-HARMONIC MAPS FROM SURFACES
Li, Yuxiang1; Wang, Youde2
2010-04-01
Source PublicationINTERNATIONAL JOURNAL OF MATHEMATICS
ISSN0129-167X
Volume21Issue:4Pages:475-495
AbstractLet f be a positive smooth function on a closed Riemann surface (M, g). The f-energy of a map u from M to a Riemannian manifold (N, h) is defined as E(f)(u) = integral(M) f vertical bar del u vertical bar(2)dV(g), and its L(2)-gradient is: tau(f)(u) = f tau(u) + del f . del u. We will study the blow-up properties of some approximate f-harmonic map sequences in this paper. For a sequence u(k) : M -> N with parallel to tau(f)(u(k))parallel to(L2) < C(1) and E(f)(u(k)) < C(2), we will show that, if the sequence is not compact, then it must blow-up at some critical points of f or some concentrate points of vertical bar tau(f)(u(k))vertical bar(2)dV(g). For a minimizing alpha-f-harmonic map sequence in some homotopy class of maps from M into N we show that, if the sequence is not compact, the blow-up points must be the minimal point of f and the energy identity holds true.
Keywordf-Harmonic map blow-up bubble alpha-harmonic map
DOI10.1142/S0129167X10006136
Language英语
Funding ProjectNational Science Foundation of China[10801082] ; Specialized Research Fund for the Doctoral Program of Higher Education[200800031078] ; 973 Project of China[2006CB805902]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000277882200005
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/10749
Collection数学所
Corresponding AuthorLi, Yuxiang
Affiliation1.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Li, Yuxiang,Wang, Youde. BUBBLING LOCATION FOR SEQUENCES OF APPROXIMATE f-HARMONIC MAPS FROM SURFACES[J]. INTERNATIONAL JOURNAL OF MATHEMATICS,2010,21(4):475-495.
APA Li, Yuxiang,&Wang, Youde.(2010).BUBBLING LOCATION FOR SEQUENCES OF APPROXIMATE f-HARMONIC MAPS FROM SURFACES.INTERNATIONAL JOURNAL OF MATHEMATICS,21(4),475-495.
MLA Li, Yuxiang,et al."BUBBLING LOCATION FOR SEQUENCES OF APPROXIMATE f-HARMONIC MAPS FROM SURFACES".INTERNATIONAL JOURNAL OF MATHEMATICS 21.4(2010):475-495.
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