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Several complex variables and CR geometry. (English) Zbl 1273.32001

Summary: 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.

MSC:

32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
32-03 History of several complex variables and analytic spaces
01A65 Development of contemporary mathematics
32T25 Finite-type domains
32T27 Geometric and analytic invariants on weakly pseudoconvex boundaries
32A70 Functional analysis techniques applied to functions of several complex variables
32V99 CR manifolds
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
32H35 Proper holomorphic mappings, finiteness theorems
32M25 Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions
32V15 CR manifolds as boundaries of domains
35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs
12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
14P05 Real algebraic sets
15B57 Hermitian, skew-Hermitian, and related matrices
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Full Text: Euclid