Blake J. Boudreaux

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20232025

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math.CV2025

Meromorphic Convexity on Complex Manifolds

Blake J Boudreaux, Rasul Shafikov

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 {\call…

math.CV2024

$T$ -polynomial convexity and holomorphic convexity

Blake J. Boudreaux

We compare the $T$ -polynomial convexity of Guedj with holomorphic convexity away from the support of $T$ . In particular we show an Oka--Weil theorem for $T$ -polynomial convexity, a…

math.CV2023

Meromorphic convexity on Stein manifolds

Blake J. Boudreaux, Rasul Shafikov

We consider generalizations of rational convexity to Stein manifolds and prove related results

math.CV2023

Hypersurface Convexity and Extension of Kähler Forms

Blake J. Boudreaux, Purvi Gupta, Rasul Shafikov

The following generalization of a result of S. Nemirovski is proved: if $X$ is either a projective or a Stein manifold and $K \subset X$ is a compact sublevel set of a strictly plur…

Meromorphic Convexity on Complex Manifolds

T-polynomial convexity and holomorphic convexity

Meromorphic convexity on Stein manifolds

Hypersurface Convexity and Extension of Kähler Forms

$T$ -polynomial convexity and holomorphic convexity