On the connectedness of the boundary of $q$-complete domains
Annales Polonici Mathematici
MSC: Primary 32F27; Secondary 32F10, 32Q60
DOI: 10.4064/ap250927-17-3
Published online: 18 May 2026
Abstract
The boundary of every relatively compact Stein domain in a complex manifold of dimension at least 2 is connected. No assumptions on the boundary regularity are necessary. The same proofs hold also for $q$-complete domains, and in the context of almost complex manifolds as well.
