## A simplification and extension of Fefferman’s theorem on biholomorphic mappings.(English)Zbl 0411.32010

### MSC:

 32D15 Continuation of analytic objects in several complex variables 32W05 $$\overline\partial$$ and $$\overline\partial$$-Neumann operators 32T99 Pseudoconvex domains 32E35 Global boundary behavior of holomorphic functions of several complex variables
Full Text:

### References:

 [1] Bedford, E., Fornaess, J.: Biholomorphic maps of weakly pseudoconvex domains. Duke Math. J.45, 711-719 (1978) · Zbl 0401.32006 [2] Bell, S.: Non-vanishing of the Bergman kernel function at boundary points of certains in ? n . Math. Ann.244, 69-74 (1979) · Zbl 0407.32011 [3] Bell. S.: A representation theorem in strictly pseudoconvex domains. In press (1980) [4] Boutet de Monvel, L., sjöstrand, J.: Sur la singularité des noyaux de Bergman et de Szegö. Soc. Mat. de France, Astérisque34-35, 123-164 (1976) · Zbl 0344.32010 [5] Diederich, K., Fornaess, J.: Pseudoconvex domains with real-analytic boundary. Ann. of Math.107, 371-384 (1978) · Zbl 0378.32014 [6] Diederich, K., Fornaess, J.: Proper holomorphic maps onto pseudoconvex domains with real analytic boundary. Preprint · Zbl 0394.32012 [7] Fefferman, C.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math.26, 1-65 (1974) · Zbl 0289.32012 [8] Folland, G., Kohn, J.J.: The Neumann problem for the Cauchy-Riemann complex. Ann. of Math. Studies, No. 75, Princeton Univ. Press 1972 · Zbl 0247.35093 [9] Kerzman, N.: The Bergman kernel. Differentiability at the boundary. Math. Ann.195, 149-158 (1972) [10] Kohn, J.J.: Harmonic integrals on strongly pseudoconvex manifolds, I and II. Ann. of Math.78, 112-148 (1963) and79, 450-472 (1964) · Zbl 0161.09302 [11] Kohn, J.J.: Sufficient conditions for subellipticity on weakly pseudoconvex domains. Proc. Nat. Acad. Sci. U.S.A.74, 2214-2216 (1977) · Zbl 0349.35011 [12] Kohn, J.J.: Subellipticity of the $$\overline \partial$$ -Neumann problem on pseudoconvex domains: sufficient conditions. Acta Math.142, 79-122 (1979) · Zbl 0395.35069 [13] Ligocka, E.: How to prove Fefferman’s theorem without use of differential geometry. Ann. Pol. Math. (to appear) · Zbl 0489.32016 [14] Ligocka, E.: Some remarks on extension of biholomorphic mappings. Proceedings of the 7-th Conference of Analytic Functions, Kozubnik, Poland 1979, Springer Lecture Notes (to appear) · Zbl 0458.32008 [15] Ligocka, E.: On boundary behavior of the Bergman kernel function for plane domains and their cartesian products (to appear) · Zbl 0577.32021 [16] Range, M.: The Caratheodory metric and holomorphic maps on a class of weakly pseudoconvex domains. Pacific J. of Math78, 173-189 (1978) · Zbl 0396.32005 [17] Webster, S.: Biholomorphic mappings and the Bergman kernel off the diagonal. Invent. Math.51, 155-169 (1979) · Zbl 0392.32013 [18] Webster, S.: On the proof of boundary smoothness of biholomorphic mappings. Preprint 1978
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.