## Kodai Mathematical Journal

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

Hiroko Kawabe

#### Abstract

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 fI: TICPn. 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 fI, $f_1^{I_1}$ and $f_{-1}^{I_{-1}}$.

#### Article information

Source
Kodai Math. J., Volume 33, Number 3 (2010), 367-382.

Dates
First available in Project Euclid: 5 November 2010

https://projecteuclid.org/euclid.kmj/1288962548

Digital Object Identifier
doi:10.2996/kmj/1288962548

Mathematical Reviews number (MathSciNet)
MR2754327

Zentralblatt MATH identifier
1214.58006

#### Citation

Kawabe, Hiroko. Harmonic maps from the Riemann sphere into the complex projective space and the harmonic sequences. Kodai Math. J. 33 (2010), no. 3, 367--382. doi:10.2996/kmj/1288962548. https://projecteuclid.org/euclid.kmj/1288962548