Illinois Journal of Mathematics

Several complex variables and CR geometry

John P. D’Angelo

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This paper discusses developments in complex analysis and CR geometry in the last forty years related to the Cauchy–Riemann equations, proper holomorphic mappings between balls, and positivity conditions in complex analysis. The paper includes anecdotes about some of the contributors to these developments.

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Illinois J. Math., Volume 56, Number 1 (2012), 7-19.

First available in Project Euclid: 27 September 2013

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Primary: 32-02: Research exposition (monographs, survey articles) 32T25: Finite type domains 32T27: Geometric and analytic invariants on weakly pseudoconvex boundaries 32A70: Functional analysis techniques [See mainly 46Exx] 32V99: None of the above, but in this section 32W05: $\overline\partial$ and $\overline\partial$-Neumann operators 32H35: Proper mappings, finiteness theorems 32M25: Complex vector fields 32V15: CR manifolds as boundaries of domains 35N15: $\overline\partial$-Neumann problem and generalizations; formal complexes [See also 32W05, 32W10, 58J10] 12D15: Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx] 14P05: Real algebraic sets [See also 12D15, 13J30] 15B57: Hermitian, skew-Hermitian, and related matrices


D’Angelo, John P. Several complex variables and CR geometry. Illinois J. Math. 56 (2012), no. 1, 7--19. doi:10.1215/ijm/1380287456.

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