arXiv subjects

Marcel K. Sucheston

Publications and source records attributed to Marcel K. Sucheston.

2 recordsLinked to original sources

arXiv2001

Plurisubharmonic defining functions, good vector fields, and exactness of a certain one form

We show that the approaches to global regularity of the d-bar Neumann problem via the methods listed in the title are equivalent when the conditions involved are suitably modified. These modified conditions are also equivalent to one that is relevant in the context of Stein neighborhood bases and Mergelyan type approximation.

math.CV↗

arXiv2000

Levi foliations in pseudoconvex boundaries and vector fields that commute approximately with d-bar

Boas and Straube proved a general sufficient condition for global regularity of the d-bar Neumann problem in terms of families of vector fields that commute approximately with d-bar. In this paper, we study the existence of these vector fields on a compact subset of the boundary whose interior is foliated by complex manifolds. This question turns out to be closely related to properties of interest from the point of view of foliation theory.

math.CV↗