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Manifold-Valued Holomorphic Approximation

Published online by Cambridge University Press:  20 November 2018

Edgar Lee Stout
Edgar Lee Stout*
Affiliation:
Department of Mathematics, The University of Washington, Seattle, WA 98195, U.S.A.e-mail: [email protected]
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Abstract

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This note considers the problem of approximating continuous maps from sets in complex spaces into complex manifolds by holomorphic maps.

Keywords

32E20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 2 , 01 June 2011 , pp. 370 - 380
Copyright
Copyright © Canadian Mathematical Society 2011

References

[1] Alexander, H., Polynomial approximation and hulls in sets of finite linear measure in ℂ n . Amer. J. Math. 93(1971), 65–74. doi:10.2307/2373448Google Scholar
[2] Chakrabarti, D., Coordinate neighborhoods of arcs and the approximation of maps into (almost) complex manifolds. Michigan Math. J. 55(2007), no. 2, 299–333. doi:10.1307/mmj/1187646996Google Scholar
[3] Chakrabarti, D., Sets of approximation and interpolation in ℂ for manifold-valued maps. J. Geom. Anal. 18(2008), no. 3, 720–739. doi:10.1007/s12220-008-9030-2Google Scholar
[4] Drinovec-Drnovšek, B. and Forstnerič, F., Approximation of holomorphic mappings on strongly pseudoconvex domains. Forum Math. 20(2008), no. 5, 817–840. doi:10.1515/FORUM.2008.039Google Scholar
[5] Duchamp, T. and Stout, E. L., Maximum modulus sets. Ann. Inst. Fourier (Grenoble) 31(1981), no. 3, v, 37–69.Google Scholar
[6] Gauthier, P. M. and Zeron, E. S., Approximation by rational mappings, via homotopy theory. Canad. Math. Bull. 49(2006), no. 2, 237–246.Google Scholar
[7] Gauthier, P. M. and Zeron, E. S., Embedding Stein manifolds and tangential approximation. Complex Var. Elliptic Equ. 51(2006), no. 8–11, 953–958. doi:10.1080/17476930600673005Google Scholar
[8] Gunning, R. C. and Rossi, H., Analytic functions of several complex variables. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965.Google Scholar
[9] Hurewicz, W. and Wallman, H., Dimension theory. Princeton Mathematical Series, 4, Princeton University Press, Princeton, NJ, 1941.Google Scholar
[10] Stout, E. L., Polynomial convexity. Progress in Mathematics, 261, Birkhäuser Boston Inc., Boston, MA, 2007.Google Scholar
[11] Zeron, E. S., Approximation and the topology of rationally convex sets. Canad. Math. Bull. 49(2006), no. 4, 628–636.Google Scholar