Holomorphic mapping of annuli in and the associated extremal function
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1979)
- Volume: 6, Issue: 3, page 381-414
- ISSN: 0391-173X
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topBedford, Eric, and Burns, Dan. "Holomorphic mapping of annuli in $C^n$ and the associated extremal function." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.3 (1979): 381-414. <http://eudml.org/doc/83814>.
@article{Bedford1979,
author = {Bedford, Eric, Burns, Dan},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Monge-Ampere foliation; strictly pseudoconvex; annulus; biholomorphism; isometry of homology; foliation},
language = {eng},
number = {3},
pages = {381-414},
publisher = {Scuola normale superiore},
title = {Holomorphic mapping of annuli in $C^n$ and the associated extremal function},
url = {http://eudml.org/doc/83814},
volume = {6},
year = {1979},
}
TY - JOUR
AU - Bedford, Eric
AU - Burns, Dan
TI - Holomorphic mapping of annuli in $C^n$ and the associated extremal function
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1979
PB - Scuola normale superiore
VL - 6
IS - 3
SP - 381
EP - 414
LA - eng
KW - Monge-Ampere foliation; strictly pseudoconvex; annulus; biholomorphism; isometry of homology; foliation
UR - http://eudml.org/doc/83814
ER -
References
top- [1] L.V. Ahlfors, Conformal Invariants : Topics in Geometric Function Theory, McGraw-Hill, New York, 1973. Zbl0272.30012MR357743
- [2] E. Bedford - M. Kalka, Foliations and complex Monge-Ampère equations, Comm. Pure Appl. Math., 30 (1977), pp. 543-571. Zbl0351.35063MR481107
- [3] E. Bedford - B.A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Inv. Math., 37 (1976), pp. 1-44. Zbl0315.31007MR445006
- [4] E. Bedford - B.A. Taylor, Variational properties of the complex Monge-Ampère equation. II: Intrinsic norms, Amer. J. Math., to appear. Zbl0446.35025MR546307
- [5] H. Cartan, Sur les fonctions de plusieurs variables complexes, Math. Z., 35 (1932), pp. 760-773. Zbl0004.40602MR1545327JFM58.0349.02
- [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. Zbl0202.11603MR254877
- [7] K. Diederich - J.E. Fornaess, Pseudoconvex domains with real-analytic boundary, Ann. of Math., 107 (1978), pp. 371-384. Zbl0378.32014MR477153
- [8] D. Eisenman, Intrinsic measures on complex manifolds and holomorphic mappings, Mem. Amer. Math. Soc., no. 96, Providence (1970). Zbl0197.05901MR259165
- [9] H. Federer, Geometric Measure Theory, Springer-Verlag, New York (1969). Zbl0176.00801MR257325
- [10] J.E. Fornaess, Embedding strictly pseudoconvex domains in convex domains, Amer. J. Math., 98 (1976), pp. 529-569. Zbl0334.32020MR422683
- [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. Zbl0194.22702MR262981
- [12] H. Huber, Über analytische Abbildungen von Ringgebieten in Ringgebiete, Compositio. Math., 9 (1951), pp. 161-168. Zbl0043.30201MR43904
- [13] H. Huber, Über analytische Abbildungen Riemannscher Flachen in sich, Comment. Math. Helv., 27 (1953), pp. 1-73. Zbl0050.08405MR54051
- [14] L.R. Hunt - J. Murray, q-plurisubharmonic functions and a generalized Dirichlet problem, Mich. Math. J., 25 (1978), pp. 299-316. Zbl0378.32013MR512901
- [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. Zbl0383.31003MR590078
- [16] N. Kerzman, A Monge-Ampère equation in complex analysis, Proceedings of Symposia in Pure Math., 30 (1977), pp. 161-167. Zbl0354.35076MR454082
- [17] H.J. Landau - R. Osserman, On analytic mappings of Riemann surfaces, J. Analyse Math., 7 (1959-60), pp. 249-279. Zbl0101.05502MR122980
- [18] R. Narasimhan, Several Complex Variables, Univ. of Chicago Press, Chicago, 1971. Zbl0223.32001MR342725
- [19] I. Naruki, On extendability of isomorphisms of Cartan connections and biholomorphic mappings of bounded domains, Tôhoku Math. J., 28 (1976), pp. 117-122. Zbl0346.32003MR402125
- [20] L. Nirenberg, Lectures on linear partial differential equations, Regional Conference Series in Mathematics, no. 17, 1973. Zbl0267.35001MR450755
- [21] R. Sacksteder, On hyper-surfaces with nonnegative sectional curvatures, Amer. J. Math., 82 (1960), pp. 609-630. Zbl0194.22701MR116292
- [22] M. Schiffer, On the modules of doubly connected domains, Quart. J. Math., 17 (1946), pp. 197-213. Zbl0060.23707MR18751
- [23] J. Siciak, Extremal plurisubharmonic functions in Cn, Proceedings of the First Finnish-Polish Summer School in Complex Analysis (1977), pp. 115-152. Zbl0384.32005MR590080
- [24] J. Siciak, A generalization of Ostrowski's theorem on lacunary power seriesBull. Acad. Polon. Sci., 8 (1976), pp. 569-574. Zbl0336.32014MR422679
- [25] J.B. Walsh, Continuity of envelopes of plurisubharmonic functions, J. Math. Mech., 18 (1968), pp. 143-148. Zbl0159.16002MR227465
- [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. MR444988
- [27] J. Kohn, Subellipticity of the ∂-Neumann problem on pseudo-convex domains, Acta Math., 142 (1979), p. 114. Zbl0395.35069
- [28] E. Bedford - J.E. Fornaess, Counterexamples to regularity for the complex Monge-Ampère equation, Inv. Math., 50 (1979), pp. 129-134. Zbl0393.35010MR517774
- [29] E. Bedford, Holomorphic mapping of products of annuli, Pacific J. Math., to appear. Zbl0449.32024MR592735
- [30] E. Bedford, Extremal plurisubharmonic functions for certain domains in C2, Indiana Univ. Math. J., to appear. Zbl0418.32015MR542948
- [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. Zbl0458.35013MR524326
- [32] W. Stoll, The characterization of strictly parabolic manifolds, Ann. Scuola Norm. Sup. Pisa, to appear. Zbl0438.32005MR577327
- [33] D. Burns, Curvatures of foliations and complex Monge-Ampère equations, in preparation.
Citations in EuDML Documents
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- Wilhelm Stoll, The characterization of strictly parabolic spaces
- Andrea Iannuzzi, Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in with real analytic boundary
- Giorgio Patrizio, Foliazioni di Monge-Ampère e classificazione olomorfa
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