Geodesic
Continuation of Complex Varieties Across Rectifiable Sets
Canadian journal of mathematics, Tome 47 (1995) no. 4, pp. 877-896

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1995-045-8
Mots-clés : 32D15, 32D20 
Xu, Yeren. Continuation of Complex Varieties Across Rectifiable Sets. Canadian journal of mathematics, Tome 47 (1995) no. 4, pp. 877-896. doi: 10.4153/CJM-1995-045-8
@article{10_4153_CJM_1995_045_8,
     author = {Xu, Yeren},
     title = {Continuation of {Complex} {Varieties} {Across} {Rectifiable} {Sets}},
     journal = {Canadian journal of mathematics},
     pages = {877--896},
     year = {1995},
     volume = {47},
     number = {4},
     doi = {10.4153/CJM-1995-045-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-045-8/}
}
TY  - JOUR
AU  - Xu, Yeren
TI  - Continuation of Complex Varieties Across Rectifiable Sets
JO  - Canadian journal of mathematics
PY  - 1995
SP  - 877
EP  - 896
VL  - 47
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-045-8/
DO  - 10.4153/CJM-1995-045-8
ID  - 10_4153_CJM_1995_045_8
ER  - 
%0 Journal Article
%A Xu, Yeren
%T Continuation of Complex Varieties Across Rectifiable Sets
%J Canadian journal of mathematics
%D 1995
%P 877-896
%V 47
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-045-8/
%R 10.4153/CJM-1995-045-8
%F 10_4153_CJM_1995_045_8

[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

[Ch] Chirka, E., Complex analytic sets, Kluwer Acad. Publ., 1989. 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

[Cu] Cullen, H., Introduction to general topology, D.C. Heath and Company, 1967. Google Scholar

[Fa] Falconer, K., The geometry of fractal sets, Cambridge Univ. Press, 1985. 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

[Ro] Rothstein, W., Zur théorie der analytischen Mengen, Math. Ann. 174(1967), 8–32. Google Scholar

[Ru] Rudin, W., Subalgebra of spaces of continuous functions, Proc. Amer. Math. Soc. 7(1956), 825–830. Google Scholar

[Sh] Shiffman, B., On the continuation of analytic sets, Math. Ann. 185(1970), 1–12. 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

Cité par Sources :