English

On the Steinness index

Complex Variables 2018-04-13 v1

Abstract

We introduce the concept of Steinness index related to the Stein neighborhood basis. We then show several results: (1) The existence of Steinness index is equivalent to that of strong Stein neighborhood basis. (2) On the Diederich-Forn{\ae}ss worm domains in particular, we present an explicit formula relating the Steinness index to the well-known Diederich-Forn{\ae}ss index. (3) The Steinness index is 1 if a smoothly bounded pseudoconvex domain admits finitely many boundary points of infinite type.

Keywords

Cite

@article{arxiv.1804.04304,
  title  = {On the Steinness index},
  author = {Jihun Yum},
  journal= {arXiv preprint arXiv:1804.04304},
  year   = {2018}
}

Comments

22 pages

R2 v1 2026-06-23T01:21:14.101Z