高维蠕虫域

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-03-25 DOI:10.1112/blms.70057

Simone Calamai, Gian Maria Dall'Ara

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引用次数: 0

摘要

我们展示了如何构造一类光滑有界伪凸区域，其边界包含给定的具有强伪凸边界的Stein流形，具有规定的余维数和D'Angelo类（测量区域边界围绕子流形的“绕”度的上同调不变量）。在这些域的设置中讨论了∂¯$\overline{\partial }$ -Neumann问题的正则性理论中的一些开放问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Higher dimensional worm domains

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Higher dimensional worm domains

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 $\bar{\partial}$ -Neumann problem are discussed in the setting of these domains.

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