Harmonic maps from the Riemann sphere into the complex projective space and the harmonic sequences

Kawabe, Hiroko

Kawabe, Hiroko

Kodai Math. J., Tome 33 (2010) no. 1, p. 367-382 / Harvested from Project Euclid

Résumé

When harmonic maps from the Riemann sphere into the complex projective space are energy bounded, it contains a subsequence converging to a bubble tree map f^I: T^I → CPⁿ. We show that their ∂-transforms and $\overline{\partial}$ -transforms are also energy bounded. Hence their subsequences converge to harmonic bubble tree maps $f_1^{I_1}:T^{I_1}$ → CPⁿ and $f_{-1}^{I_{-1}}:T^{I_{-1}}$ → CPⁿ respectively. In this paper, we show relations between f^I, $f_1^{I_1}$ and $f_{-1}^{I_{-1}}$ .

Publié le : 2010-10-15
Classification:

@article{1288962548,
     author = {Kawabe, Hiroko},
     title = {Harmonic maps from the Riemann sphere into the complex projective space and the harmonic sequences},
     journal = {Kodai Math. J.},
     volume = {33},
     number = {1},
     year = {2010},
     pages = { 367-382},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1288962548}
}

Kawabe, Hiroko. Harmonic maps from the Riemann sphere into the complex projective space and the harmonic sequences. Kodai Math. J., Tome 33 (2010) no. 1, pp.  367-382. http://gdmltest.u-ga.fr/item/1288962548/