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Continuation of Complex Varieties Across Rectifiable Sets
Published online by Cambridge University Press: 20 November 2018
Abstract
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We continue our research on extension of complex varieties across closed subsets. While efforts are being made to deal with varieties of any dimensions, the paper primarily concerns 1-dimensional case, and the exceptional set is thus assumed to be connected with finite length. As applications of the main result, several corollaries are obtained with interesting features.
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- Copyright © Canadian Mathematical Society 1995
References
[AU] Alexander, H., Polynomial hulls and linear measure, Lecture Notes in Math.
1276(1987), 1–11.Google Scholar
[A12] Alexander, H., Areas of projections of analytic sets, Invent. Math.
16(1972), 335–341.Google Scholar
[A13] Alexander, H., The ends of varieties, preprint.Google Scholar
[Be] Besicovitch, A., On the fundamental geometric properties of linear measurable plane sets of points, II, Math. Ann.
115(1938), 296–329.Google Scholar
[CK] Chirka, E., and Henkin, G., Boundary properties of holomorphic functions of several complex variables, J. Soviet Math.
5(1976), 612–687.Google Scholar
[Fo] Forstneric, F., Regularity of varieties in strictly pseudoconvex domains, Publ. Mat.
32(1988), 145–150.Google Scholar
[GS] Globevnik, J., and Stout, E., The ends of discs, Bull. Soc. Math. France
114(1986), 175–195.Google Scholar
[Gl] Goluzin, G., Geometric theory of functions of a complex variable, Amer. Math. Soc, 1969.Google Scholar
[La] Lawrence, M., Polynomial hulls and geometric function theory of several complex variables, Ph.D Thesis. Univ. of Washington, 1991.Google Scholar
[Po] Pommerenke, Ch., On analytic functions with cluster sets of finite linear measure, Michigan Math. J.
34(1987), 93–97.Google Scholar
[Ru] Rudin, W., Subalgebra of spaces of continuous functions, Proc. Amer. Math. Soc.
7(1956), 825–830.Google Scholar
[Sh2] Shiffman, B., On the removal of singularities of analytic sets, Michigan Math. J.
15(1970), 111–120.Google Scholar
[St] Stout, E., The theory of uniform algebras, Bogden and Quigley, Inc., Publ., 1971.Google Scholar
[Wa] Wazewski, T., Rectifiable continua in connection with absolutely continuous functions and mappings, (Polish). Ann. Polon. Math.
3(1927), 9–49.Google Scholar
[We] Wermer, J., Polynomial approximation on an arc in, ℂ3, Ann. Math.
62(1955), 269–270.Google Scholar
[Xu] Xu, Y., Extension of complex varieties across C1 manifolds, Michigan Math. J.
40(1993), 399–410.Google Scholar
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