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arXiv · 2510.27100

Meromorphic Convexity on Complex Manifolds

Blake J Boudreaux·Rasul Shafikov
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Abstract

The notion of meromorphic convexity is defined and studied on complex manifolds. Using this notion, in analogy with Stein manifolds, a new class of complex manifolds, called {\calligra M }-manifolds, is introduced. This is a class of complex manifolds with a good supply of global meromorphic functions, in particular, it includes all Stein manifolds and projective manifolds. It is also shown that there exist noncompact complex manifolds, known as long $\mathbb C^2$, that are {\calligra M }-manifolds but do not contain any nonconstant holomorphic functions.

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Blake J Boudreaux, Rasul Shafikov. 2025-10-31. Meromorphic Convexity on Complex Manifolds. https://arxiv.org/abs/2510.27100

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