We show how to construct a class of smooth bounded pseudoconvex domains whose boundary contains a given Stein manifold with strongly pseudoconvex boundary, having a prescribed codimension and D'Angelo class (a cohomological invariant measuring the “winding” of the boundary of the domain around the submanifold). Some open questions in the regularity theory of the (Formula presented.) -Neumann problem are discussed in the setting of these domains.
Higher dimensional worm domains / Calamai, Simone; Dall'Ara, Gian Maria. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - STAMPA. - 57:(2025), pp. 1718-1728. [10.1112/blms.70057]
Higher dimensional worm domains
Calamai, Simone;
2025
Abstract
We show how to construct a class of smooth bounded pseudoconvex domains whose boundary contains a given Stein manifold with strongly pseudoconvex boundary, having a prescribed codimension and D'Angelo class (a cohomological invariant measuring the “winding” of the boundary of the domain around the submanifold). Some open questions in the regularity theory of the (Formula presented.) -Neumann problem are discussed in the setting of these domains.
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