Holomorphic mapping of annuli in C n and the associated extremal function
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 6 (1979) no. 3, pp. 381-414.
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     author = {Bedford, Eric and Burns, Dan},
     title = {Holomorphic mapping of annuli in $C^n$ and the associated extremal function},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {381--414},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 6},
     number = {3},
     year = {1979},
     mrnumber = {553791},
     zbl = {0422.32021},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1979_4_6_3_381_0/}
}
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Bedford, Eric; Burns, Dan. Holomorphic mapping of annuli in $C^n$ and the associated extremal function. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 6 (1979) no. 3, pp. 381-414. http://www.numdam.org/item/ASNSP_1979_4_6_3_381_0/

[1] L.V. Ahlfors, Conformal Invariants : Topics in Geometric Function Theory, McGraw-Hill, New York, 1973. | MR | Zbl

[2] E. Bedford - M. Kalka, Foliations and complex Monge-Ampère equations, Comm. Pure Appl. Math., 30 (1977), pp. 543-571. | MR | Zbl

[3] E. Bedford - B.A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Inv. Math., 37 (1976), pp. 1-44. | MR | Zbl

[4] E. Bedford - B.A. Taylor, Variational properties of the complex Monge-Ampère equation. II: Intrinsic norms, Amer. J. Math., to appear. | MR | Zbl

[5] H. Cartan, Sur les fonctions de plusieurs variables complexes, Math. Z., 35 (1932), pp. 760-773. | JFM | MR | Zbl

[6] S.S. Chern - H.I. Levine - L. Nirenberg, Intrinsic norms on a complex manifold, Global Analysis. Papers in Honor of K. Kodaira, Princeton Univ. Press (1969), pp. 119-139. | MR | Zbl

[7] K. Diederich - J.E. Fornaess, Pseudoconvex domains with real-analytic boundary, Ann. of Math., 107 (1978), pp. 371-384. | MR | Zbl

[8] D. Eisenman, Intrinsic measures on complex manifolds and holomorphic mappings, Mem. Amer. Math. Soc., no. 96, Providence (1970). | MR | Zbl

[9] H. Federer, Geometric Measure Theory, Springer-Verlag, New York (1969). | MR | Zbl

[10] J.E. Fornaess, Embedding strictly pseudoconvex domains in convex domains, Amer. J. Math., 98 (1976), pp. 529-569. | MR | Zbl

[11] P. Hartman, On the isometric immersions in euclidean space of manifolds with nonnegative sectional curvatures, Trans. Amer. Math. Soc., 147 (1970), pp. 529-540. | MR | Zbl

[12] H. Huber, Über analytische Abbildungen von Ringgebieten in Ringgebiete, Compositio. Math., 9 (1951), pp. 161-168. | EuDML | Numdam | MR | Zbl

[13] H. Huber, Über analytische Abbildungen Riemannscher Flachen in sich, Comment. Math. Helv., 27 (1953), pp. 1-73. | EuDML | MR | Zbl

[14] L.R. Hunt - J. Murray, q-plurisubharmonic functions and a generalized Dirichlet problem, Mich. Math. J., 25 (1978), pp. 299-316. | MR | Zbl

[15] B. Josefson, On the equivalence between locally polar and globally polar sets for plurisubharmonic functions on Cn, Ark. Mat., 16 (1978), pp. 109-115. | MR | Zbl

[16] N. Kerzman, A Monge-Ampère equation in complex analysis, Proceedings of Symposia in Pure Math., 30 (1977), pp. 161-167. | MR | Zbl

[17] H.J. Landau - R. Osserman, On analytic mappings of Riemann surfaces, J. Analyse Math., 7 (1959-60), pp. 249-279. | MR | Zbl

[18] R. Narasimhan, Several Complex Variables, Univ. of Chicago Press, Chicago, 1971. | MR | Zbl

[19] I. Naruki, On extendability of isomorphisms of Cartan connections and biholomorphic mappings of bounded domains, Tôhoku Math. J., 28 (1976), pp. 117-122. | MR | Zbl

[20] L. Nirenberg, Lectures on linear partial differential equations, Regional Conference Series in Mathematics, no. 17, 1973. | MR | Zbl

[21] R. Sacksteder, On hyper-surfaces with nonnegative sectional curvatures, Amer. J. Math., 82 (1960), pp. 609-630. | MR | Zbl

[22] M. Schiffer, On the modules of doubly connected domains, Quart. J. Math., 17 (1946), pp. 197-213. | MR | Zbl

[23] J. Siciak, Extremal plurisubharmonic functions in Cn, Proceedings of the First Finnish-Polish Summer School in Complex Analysis (1977), pp. 115-152. | MR | Zbl

[24] J. Siciak, A generalization of Ostrowski's theorem on lacunary power series Bull. Acad. Polon. Sci., 8 (1976), pp. 569-574. | MR | Zbl

[25] J.B. Walsh, Continuity of envelopes of plurisubharmonic functions, J. Math. Mech., 18 (1968), pp. 143-148. | MR | Zbl

[26] V.P. Zaharjuta, Extremal plurisubharmonic functions, orthogonal polynomials and the Bernstein-Walsh theorem for analytic functions of s.c.v., Ann. Pol. Math., 33 (1976), pp. 137-148. | MR

[27] J. Kohn, Subellipticity of the ∂-Neumann problem on pseudo-convex domains, Acta Math., 142 (1979), p. 114. | MR | Zbl

[28] E. Bedford - J.E. Fornaess, Counterexamples to regularity for the complex Monge-Ampère equation, Inv. Math., 50 (1979), pp. 129-134. | EuDML | MR | Zbl

[29] E. Bedford, Holomorphic mapping of products of annuli, Pacific J. Math., to appear. | MR | Zbl

[30] E. Bedford, Extremal plurisubharmonic functions for certain domains in C2, Indiana Univ. Math. J., to appear. | MR | Zbl

[31] R. Moriyón, Regularity for the Dirichlet problem for the complex Monge-Ampère equation det (ujk) = 0, Proc. Nat. Acad. Sci. U.S.A., to appear. | MR

[32] W. Stoll, The characterization of strictly parabolic manifolds, Ann. Scuola Norm. Sup. Pisa, to appear. | EuDML | Numdam | MR | Zbl

[33] D. Burns, Curvatures of foliations and complex Monge-Ampère equations, in preparation.