Kodai Mathematical Journal

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

Hiroko Kawabe

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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

Permanent link to this document
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


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