The Levi Problem in \mathbb Cⁿ: A Survey

2014/11/03 by Harry J. Slatyer, Slatyer, Harry J.
Mathematics · #32-01 (Secondary) #32E40 (Primary) #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1411.0363

openalex publication_date 2014/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss domains of holomorphy and several notions of pseudoconvexity (drawing parallels with the corresponding notions from geometric convexity), and present a mostly self-contained solution to the Levi problem. We restrict our attention to domains of \mathbb Cⁿ.

Related

• Levi equation and local maximum property
• Cartan-Thullen theorem and Levi problem in context of generalised convexity
• Convex domains with locally Levi-flat boundaries
• Levi-flats in \mathbbCPⁿ: a survey for nonexperts
• On nondegeneracy conditions for the Levi map in higher codimension: a\n survey