zbMATH — the first resource for mathematics

Boundary regularity of proper holomorphic mappings. (English) Zbl 0501.32010

32D15 Continuation of analytic objects in several complex variables
32A40 Boundary behavior of holomorphic functions of several complex variables
32T99 Pseudoconvex domains
32H99 Holomorphic mappings and correspondences
32E35 Global boundary behavior of holomorphic functions of several complex variables
Full Text: DOI EuDML
[1] Bell, S.: Non-vanishing of the Bergman kernel function at boundary points of certain domains in ? n . Math. Ann.244, 69-74 (1979) · Zbl 0407.32011
[2] Bell, S., Ligocka, E.: A simplification and extension of Fefferman’s theorem on biholomorphic mappings. Invent. Math.57, 283-289 (1980) · Zbl 0421.32015
[3] Bell, S., Boas, H.: Regularity of the Bergman projection in weakly pseudoconvex domains. Math. Ann.257, 23-40 (1981) · Zbl 0461.32007
[4] Bell, S.: Biholomorphic mappings and the \(\bar \partial \) -problem. Annals Math.114, 103-113 (1981) · Zbl 0423.32009
[5] Bell, S.: Proper holomorphic mappings and the Bergman projection. Duke Math. J.48, 167-175 (1981) · Zbl 0465.32014
[6] Bell, S.: The Bergman kernel function and proper holomorphic mappings. Preprint 1981 · Zbl 0465.32014
[7] Bell, S., Catlin, D.: Proper holomorphic mappings extend smoothly to the boundary. Bulletin of AMS6 (1982) (To appear) · Zbl 0491.32018
[8] Cartan, H.: Sur les transformations analytiques des domaines cerclés et semi-cerclés bornés. Math. Ann.106 (1932)
[9] Diederich, K., Fornaess, J.E.: Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions. Invent. Math.39, 129-141 (1977) · Zbl 0353.32025
[10] Diederich, K., Fornaess, J.E.: Pseudoconvex domains with real-analytic boundary. Annals Math.107, 371-384 (1978) · Zbl 0378.32014
[11] Diederich, K., Fornaess, J.E.: A remark on a paper of Bell. Manuscripta math.34, 31-44 (1981) · Zbl 0462.32006
[12] Diederich, K., Fornaess, J.E.: Proper holomorphic images of strictly pseudoconvex domains. Math. Ann.259, 279-286 (1982) · Zbl 0486.32013
[13] Diederich, K., Fornaess, J.E.: Smooth extendability of proper holomorphic mappings. Bulletin of AMS6 (1982) (To appear) · Zbl 0521.32014
[14] Diederich, K., Fornaess, J.E., Pflug, P.: Convexity in Complex Analysis. Forthcoming book
[15] Fefferman, Ch.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math.26, 1-65 (1974) · Zbl 0289.32012
[16] Kaup, W.: Über das Randverhalten von holomorphen Automorphismen beschränkter Gebiete. Manuscripta math.3, 257-270 (1970) · Zbl 0202.36504
[17] Kohn, J.J.: Harmonic integrals on strongly pseudoconvex manifolds, I and II, Annals Math.78, 112-148 (1963),79, 450-472 (1964) · Zbl 0161.09302
[18] Kohn, J.J.: Subellipticity of the \(\bar \partial \) -Neumann problem on pseudo-convex domains: sufficient conditions. Acta Math.142, 79-122 (1979) · Zbl 0395.35069
[19] Ligocka, E.: How to prove Fefferman’s theorem without use of differential geometry. Ann. Pol. Math. · Zbl 0489.32016
[20] Nirenberg, L., Webster, S.M., Yang, P.: Local boundary regularity of holomorphic mappings. Comm. Pure and Appl. Math.33, 305-338 (1980) · Zbl 0436.32018
[21] Chee, P.S.: The Blaschke condition for bounded holomorphic functions. Trans. AMS148, 249-263 (1970) · Zbl 0196.09503
[22] Rudin, W.: Function theory on the ball. Grundlehren der Mathematischen Wissenschaften, Vol. 241. Berlin-Heidelberg-New York: Springer 1980 · Zbl 0495.32001
[23] Webster, S.: On the proof of boundary smoothness of biholomorphic mappings. Preprint 1978
[24] Webster, S.: Biholomorphic mappings and the Bergman kernel off the diagonal. Invent. Math.51, 155-169 (1979) · Zbl 0392.32013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.