Opuscula Math. 46, no. 4 (2026), 513-520
https://doi.org/10.7494/OpMath.202607111
Opuscula Mathematica
One complex variable versus several complex variables: The Hartogs extension phenomenon in context
Abstract. We explicate the difference between the function theory of one complex variable and the function theory of several complex variables. In particular, we use the inhomogeneous Cauchy-Riemann equations to explain why there is a Hartogs extension phenomenon in several complex variables but not in one complex variable.
Keywords: domain, Hartogs extension phenomenon, Cauchy-Riemann equations.
Mathematics Subject Classification: 30-02, 30A99, 32A99, 32T05.
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- Steven G. Krantz
https://orcid.org/0000-0003-0902-2014- Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri, USA 63130
- Communicated by Vicenţiu D. Rădulescu.
- Received: 2026-05-29.
- Revised: 2026-07-09.
- Accepted: 2026-07-11.
- Published online: 2026-08-04.
