Blake J. Boudreaux

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math.CV2026

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

Hypersurface Convexity and Extension of KÃ¤hler 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…

math.CV2024

Relationships Between the Bergman Kernels of Hartogs Domains and Their Base

Blake J. Boudreaux

We explore the relationship between the Bergman kernel of a Hartogs domain and weighted Bergman kernels over its base domain. In particular we develop a representation of the Bergm…

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…

Meromorphic Convexity on Complex Manifolds

Hypersurface Convexity and Extension of KÃ¤hler Forms

Relationships Between the Bergman Kernels of Hartogs Domains and Their Base

T-polynomial convexity and holomorphic convexity

$T$ -polynomial convexity and holomorphic convexity