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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Stability of polynomial convexity of totally real sets
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by Franc Forstnerič PDF
Proc. Amer. Math. Soc. 96 (1986), 489-494 Request permission

Abstract:

We show that certain compact polynomially convex subsets of ${\mathbb {C}^n}$ remain polynomially convex under sufficiently small ${{\mathbf {C}}^2}$ perturbations.
References
  • John Erik Fornaess, Embedding strictly pseudoconvex domains in convex domains, Amer. J. Math. 98 (1976), no. 2, 529–569. MR 422683, DOI 10.2307/2373900
  • F. Reese Harvey and R. O. Wells Jr., Holomorphic approximation and hyperfunction theory on a $C^{1}$ totally real submanifold of a complex manifold, Math. Ann. 197 (1972), 287–318. MR 310278, DOI 10.1007/BF01428202
  • F. Reese Harvey and R. O. Wells Jr., Zero sets of non-negative strictly plurisubharmonic functions, Math. Ann. 201 (1973), 165–170. MR 330510, DOI 10.1007/BF01359794
  • L. Hörmander, An introduction to complex analysis in several variables, North-Holland, Amsterdam and London, 1973. G. M. Khenkin and E. M. Čirka, Boundary properties of holomorphic functions of several complex variables, Sovremeni Problemi Mat. 4, Moskva 1975, pp. 13-142; English transl., Soviet Math. J. 5 (1976), no. 5, 612-687. (Russian)
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 96 (1986), 489-494
  • MSC: Primary 32E20
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0822446-2
  • MathSciNet review: 822446