Levi equation and local maximum property

2024/09/09 by Giuseppe Della Sala, Della Sala, Giuseppe, Giuseppe Tomassini +1
Mathematics · #32C35 #32Q99 #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2409.05776

openalex publication_date 2024/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of the paper is to study the level sets of the solutions of Dirichlet problems for the Levi operator on strongly pseudoconvex domains Ω in \mathbb C². Such solutions are generically non smooth, and the geometric properties of their level sets are characterized by means of hulls of their intersections with bΩ, using as main tool the local maximum property introduced by Slodkowski (PJM, 1988). The same techniques are then employed to study the behavior of the complete Levi operator for graphs in \mathbb C².

Related

• The Levi Problem in \mathbb Cⁿ: A Survey
• Levi Problem in Complex Manifolds
• A characterization of domains in \Cⁿ with locally Levi-flat boundaries
• Bounding smooth Levi-flat hypersurfaces in a Stein manifold
• Convex domains with locally Levi-flat boundaries