D’Angelo, John P. Several complex variables and CR geometry. (English) Zbl 1273.32001 Ill. J. Math. 56, No. 1, 7-19 (2012). 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 Keywords:CR geometry; \(\overline\partial\)-Neumann problem; finite type; subelliptic estimates; proper mappings between balls PDFBibTeX XMLCite \textit{J. P. D'Angelo}, Ill. J. Math. 56, No. 1, 7--19 (2012; Zbl 1273.32001) Full Text: Euclid