DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-28

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Levi pseudoconvex domains

Definition

Let $Ω \subseteq C^{m}$ be a domain with $C^{2}$ boundary. We say that $Ω$ is Levi pseudoconvex when for every boundary point $p \in \partial Ω$ there are a neighbourhood $U$ of $p$ and a function $ρ \in C^{2} (U, R)$ such that

$Ω \cap U = {z \in U : ρ (z) < 0}, d ρ (p) \neq 0,$

and

$L_{ρ} (p; v) \geq 0$

for every complex tangent vector $v \in C^{m}$ satisfying

$\sum_{j = 1}^{m} \frac{\partial ρ}{\partial z_{j}} (p) v_{j} = 0.$

Depends on

The Levi form and strict plurisubharmonicity

Used by

Dependency tree · one level

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Sources

Jiří Lebl, Tasty Bits of Several Complex Variables, §2.3 and §2.5 (standard reference, not scraped)
Harold P. Boas, Lecture Notes on Several Complex Variables, §3.3.1 (standard reference, not scraped)