BUBBLING LOCATION FOR SEQUENCES OF APPROXIMATE f-HARMONIC MAPS FROM SURFACES
2010 ◽
Vol 21
(04)
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pp. 475-495
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Keyword(s):
Blow Up
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Let 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 [Formula: see text] and its L2-gradient is: [Formula: see text] We will study the blow-up properties of some approximate f-harmonic map sequences in this paper. For a sequence uk : M → N with ‖τf(uk)‖L2 < C1 and Ef(uk) < C2, 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 |τf(uk)|2dVg. For a minimizing α-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.
1994 ◽
Vol 36
(1)
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pp. 77-80
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2017 ◽
Vol 14
(07)
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pp. 1750098
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2000 ◽
Vol 68
(2)
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pp. 145-154
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1993 ◽
Vol 04
(02)
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pp. 359-365
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Keyword(s):
2005 ◽
Vol 16
(09)
◽
pp. 1017-1031
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2012 ◽
Vol 23
(09)
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pp. 1250095
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1998 ◽
Vol 09
(07)
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pp. 821-844
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