Carathéodory extremal maps of ellipsoids

Daowei MA

doi:10.2969/jmsj/04940723

Daowei MA

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 4 Pages 723-739

DOI https://doi.org/10.2969/jmsj/04940723

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Published: 1997 Received: September 11, 1995 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : BED) E. Bedford, On the automorphism group of a Stein manifold, Math. Ann., 266 (1983), 215-227.
CAR) C. Carathéodory, Über die abbildungen, die durch systeme von analytischen funktionen von mehreren veranderlichen erzeugt werden, Math. Z., 34 (1932), 758-792.
DIT) S. Dineen and R.M. Timoney, Extremal mappings for the Schwarz lemma, preprint.
FRI) B.L. Fridman, Biholomorphic invariants of a hyperbolic manifold and some applications, Trans. Amer. Math. Soc., 276 (1983), 685-698.
GMW) I. Graham and H. Wu, Characterizations of the unit ball Bⁿ in complex euclidean space, Math. Z., 189 (1985), 449-456.
HAR) L.A. Harris, Schwarz's lemma and the maximum principle in infinite dimensional spaces, Ph. D. Thesis, Cornell University, 1969.
JOH) F. John, Extremum problems with inequalities as subsidiary conditions, In: R. Courant Anniversary Volume, (pp. 187-204), New York: Interscience, 1948.
KER) N. Kerzman and J.-P. Rosay, Fonctions plurisousharmoniques d'exhaustion bornées et domaines taut, Math. Ann., 257 (1981), 171-184.
KOB) S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, New York: Marcel Dekker, 1970.
KUB) Y. Kubota, An extremal problem on bounded symmetric domains, Bull. London Math. Soc., 15 (1983), 126-130.
MIL) J.W. Milnor, Morse theory, Princeton, New Jersey: Princeton University Press, 1963.
RAB) V.V. Rabotin, Carathéodory extremal problem in the class of holomorphic mappings of bounded circular domains, Sibirskii Matematicheskii Zhurnal. 27 (1986), 143-149.
ROY) H.L. Royden, Remarks on the Kobayashi metric, In: Proc. Maryland conference on several complex variables (Lecture Notes Math., vol. 185, pp. 136-207), Berlin-Heidelberg-New York: Springer, 1987.
RUD) W. Rudin, Function theory in the unit ball of Cⁿ, Berlin-Heidelberg-New York: Springer, 1980.
SAD) A. Sadullaev, The Schwarz lemma for circular domains and its applications, Mat. Zametki, 27 (1980), 245-253.
SHI) Y. Shikata, On a distance function on the set of differentiable structures, Osaka J. Math., 3 (1966), 65-79.
SIB) N. Sibony, Remarks on the Kobayashi metric, unpublished notes, 1982.
TRA) G. Travaglini, An analogue of the Schwarz lemma for bounded symmetric domains, Proc. Amer. Math. Soc., 88 (1983), 85-88.
WIN) J. Winkelmann, Semicontinuity results for the topology of taut manifolds, preprint. [WUH) H. Wu, Normal families of holomorphic mappings, Acta Math., 119 (1967), 193-233.
ZL1) M.G. Zaidenberg and V.J. Lin, On bounded domains of holomorphy that are not holomorphically contractible, Soviet Math. Dokl., 20 (1979), 1262-1266.
ZL2) M.G. Zaidenberg and V.J. Lin, Finiteness theorems for holomorphic maps, In: Khenkin, G.M. (ed.), Several Complex Variables III, (Encyclopaedia of Mathematical Sciences, vol. 9, pp. 113-172), Moscow: Publisher VINITI, 1986 (English translation, Springer-Verlag, 1989).

Right : [BED] E. Bedford, On the automorphism group of a Stein manifold, Math. Ann., 266 (1983), 215-227.
[CAR] C. Carathéodory, Über die abbildungen, die durch systeme von analytischen funktionen von mehreren veranderlichen erzeugt werden, Math. Z., 34 (1932), 758-792.
[DIT] S. Dineen and R. M. Timoney, Extremal mappings for the Schwarz lemma, preprint.
[FRI] B. L. Fridman, Biholomorphic invariants of a hyperbolic manifold and some applications, Trans. Amer. Math. Soc., 276 (1983), 685-698.
[GMW] I. Graham and H. Wu, Characterizations of the unit ball Bⁿ in complex euclidean space, Math. Z., 189 (1985), 449-456.
[HAR] L. A. Harris, Schwarz's lemma and the maximum principle in infinite dimensional spaces, Ph. D. Thesis, Cornell University, 1969.
[JOH] F. John, Extremum problems with inequalities as subsidiary conditions, In: R. Courant Anniversary Volume, (pp. 187-204), New York: Interscience, 1948.
[KER] N. Kerzman and J. -P. Rosay, Fonctions plurisousharmoniques d'exhaustion bornées et domaines taut, Math. Ann., 257 (1981), 171-184.
[KOB] S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, New York: Marcel Dekker, 1970.
[KUB] Y. Kubota, An extremal problem on bounded symmetric domains, Bull. London Math. Soc., 15 (1983), 126-130.
[MIL] J. W. Milnor, Morse theory, Princeton, New Jersey: Princeton University Press, 1963.
[RAB] V. V. Rabotin, Carathéodory extremal problem in the class of holomorphic mappings of bounded circular domains, Sibirskii Matematicheskii Zhurnal. 27 (1986), 143-149.
[ROY] H. L. Royden, Remarks on the Kobayashi metric, In: Proc. Maryland conference on several complex variables (Lecture Notes Math., vol. 185, pp. 136-207), Berlin-Heidelberg-New York: Springer, 1987.
[RUD] W. Rudin, Function theory in the unit ball of Cⁿ, Berlin-Heidelberg-New York: Springer, 1980.
[SAD] A. Sadullaev, The Schwarz lemma for circular domains and its applications, Mat. Zametki, 27 (1980), 245-253.
[SHI] Y. Shikata, On a distance function on the set of differentiable structures, Osaka J. Math., 3 (1966), 65-79.
[SIB] N. Sibony, Remarks on the Kobayashi metric, unpublished notes, 1982.
[TRA] G. Travaglini, An analogue of the Schwarz lemma for bounded symmetric domains, Proc. Amer. Math. Soc., 88 (1983), 85-88.
[WIN] J. Winkelmann, Semicontinuity results for the topology of taut manifolds, preprint.
[WUH) H. Wu, Normal families of holomorphic mappings, Acta Math., 119 (1967), 193-233.
[ZL1] M. G. Zaidenberg and V. J. Lin, On bounded domains of holomorphy that are not holomorphically contractible, Soviet Math. Dokl., 20 (1979), 1262-1266.
[ZL2] M. G. Zaidenberg and V. J. Lin, Finiteness theorems for holomorphic maps, In: Khenkin, G. M. (ed.), Several Complex Variables III, (Encyclopaedia of Mathematical Sciences, vol. 9, pp. 113-172), Moscow: Publisher VINITI, 1986 (English translation, Springer-Verlag, 1989).

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