Convex domain

Definition

In one dimension

A domain (open connected subset) in $\mathbb {C}$ is termed convex if given any two points in the domain, the entire line segment joining those two points is also in the domain.

In higher dimensions

A domain in $\mathbb {C} ^{n}$ is termed convex if given any two points in the domain, the entire line segment joining those two points is also in the domain.

Relation with other properties

Stronger properties

• Disc
• Polydisc

Weaker properties

• Star-like domain
• Contractible domain
• Holomorphically convex domain
• Simply connected domain