Abstract
Rational proper holomorphic maps from the unit ball in ℂ2 into the unit ball ℂN with degree 2 are studied. Any such map must be equivalent to one of the four types of maps.
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References
Faran J. Maps from the two ball to the three ball. Invent Math, 1982, 68: 441–475
D’Angelo J P. Proper holomorphic mappings between balls of different dimensions. Mich Math J, 1988, 35: 83–90
Wono S B. Proper holomorphic mappings in Several Complex Variables. P D thesis. Urbana-Champaign: University of Illinois, 1993
Huang X. On a linearity problem of proper holomorphic mappings between balls in complex spaces of different dimensions. J of Diff Geom, 1999, 51(1): 13–33
Huang X. On a semi-rigidity property for holomorphic maps. Asian J Math, 2003, 7: 463–492
Ji S, Xu D. Rational maps between \(\mathbb{B}^n \) and \(\mathbb{B}^N \) with geometric rank κ 0 ≤ n − 2 and minimal target dimension. Asian J Math, 2004, 8: 233–258
Huang X, Ji S, Xu D. Several results for holomorphic mappings from \(\mathbb{B}^n \) into \(\mathbb{B}^N \). Contemporary Math (A special issue in honor of Professor F. Treves), 2005, 368: 267–292
Huang X, Ji S, Xu D. A new gap phenomemon for proper mapping from \(\mathbb{B}^n \) into \(\mathbb{B}^N \). Math Research Letter, 2006, 4: 515–529
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Dedicated to Professor Sheng GONG on the occasion of his 75th birthday
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Chen, Z., Ji, S. & Xu, D. Rational holomorphic maps from \(\mathbb{B}^2 \) into \(\mathbb{B}^N \) with degree 2. SCI CHINA SER A 49, 1504–1522 (2006). https://doi.org/10.1007/s11425-006-2057-6
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DOI: https://doi.org/10.1007/s11425-006-2057-6