English

Q-pseudoconvex and q-holomorphically convex domains

Complex Variables 2018-09-05 v1

Abstract

In this article we prove a global result in the spirit of Basener's theorem regarding the relation between q-pseudoconvexity and q-holomorphic convexity: we prove that any smoothly bounded strictly q-pseudoconvex open subset of the complex Euclidean space is (q + 1)-holomorphically convex; moreover, assuming that the given open set verifies an additional assumption, we prove that it is q-holomorphically convex. We also prove that any open subset of the complex n-dimensional Euclidean space is n-holomorphically convex.

Keywords

Cite

@article{arxiv.1809.00728,
  title  = {Q-pseudoconvex and q-holomorphically convex domains},
  author = {George-Ionut Ionita and Ovidiu Preda},
  journal= {arXiv preprint arXiv:1809.00728},
  year   = {2018}
}

Comments

7 pages

R2 v1 2026-06-23T03:53:07.457Z