Smoothness to the Boundary of Biholomorphic Mappings
Main Article Content
Abstract
Under a plausible geometric hypothesis, we show that a biholomorphic mappingof smoothly bounded, pseudoconvex domains extends to a diffeomorphism of the closures.
Article Details
References
- R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
- S. R. Bell, Biholomorphic mappings and the ∂ problem, Ann. Math., 114(1981), 103-113.
- S. R. Bell, Local boundary behavior of proper holomorphic mappings, Complex Analysis of Several Variables (Madison, Wis., 1982), 1-7, Proc. Sympos. Pure Math., 41, Amer. Math. Soc., Providence, RI, 1984.
- S. R. Bell and E. Ligocka, A simplification and extension of Fefferman's theorem on biholomorphic mappings, Invent. Math. 57(1980), 283-289.
- R. B. Burckel, An Introduction to Classical Complex Analysis, Academic Press, New York, 1979.
- K. Diederich and J. E. Fornæss, Pseudoconvex domains: Bounded strictly plurisubharmonic exhaustion functions, Invent. Math. 39(1977), 129-141.
- C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26(1974), 1-65.
- G. B. Folland and J. J. Kohn, The Neumann Problem for the Cauchy-Riemann Complex, Princeton University Press, Princeton, 1972.
- B. Fridman, Biholomorphic transformations that do not extend continuously to the boundary, Michigan Math. J. 38(1991), 67-73.
- G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, American Mathematical Society, Providence, 1969.
- R. E. Greene and S. G. Krantz, Function Theory of One Complex Variable, 3rd ed., American Mathematical Society, Providence, RI, 2006.
- G. M. Henkin, An analytic polyhedron is not holomorphically equivalent to a strictly pseudoconvex domain, (Russian) Dokl. Akad. Nauk SSSR 210(1973), 1026-1029.
- L. H ¨ormander, L2 estimates and existence theorems for the ∂ operator, Acta Math. 113(1965), 89-152. w
- J. J. Kohn, Global regularity for ∂ on weakly pseudo-convex manifolds, Trans. AMS 181(1973), 273-292.
- S. G. Krantz, Function Theory of Several Complex Variables, 2nd ed., American Mathematical Society, Providenc, RI, 2001.
- R. M. Range, The Carath ´eodory metric and holomorphic maps on a class of weakly pseudoconvex domains, Pacific J. Math. 78(1978), 173-189.
- R. M. Range, A remark on bounded strictly plurisubharmonic exhaustion functions, Proc. AMS 81(1981), 220-222.
- S. Roman, The formula of Fa`a di Bruno, Am. Math. Monthly 87(1980), 805-809.
- E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993.