5 citations · 5 across the 7 of their papers we have counts for
8 papers
Nonprojective -manifolds
Blake Boudreaux, Rasul Shafikov
In a previous paper, the authors introduced, by analogy with Stein manifolds, a class of complex manifolds called -manifolds. This class contains all complex projectiv…
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…
-polynomial convexity and holomorphic convexity
Blake J. Boudreaux
We compare the -polynomial convexity of Guedj with holomorphic convexity away from the support of . In particular we show an Oka--Weil theorem for -polynomial convexity, a…
Meromorphic convexity on Stein manifolds
Blake J. Boudreaux, Rasul Shafikov
We consider generalizations of rational convexity to Stein manifolds and prove related results
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 is either a projective or a Stein manifold and is a compact sublevel set of a strictly plur…
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…
On Rational Convexity of Totally Real Sets
Blake J. Boudreaux, Rasul Shafikov
Under a mild technical assumption, we prove a necessary and sufficient condition for a totally real compacdt set in to be rationally convex. This generalizes a class…
Equivalent Bergman Spaces with Inequivalent Weights
Blake J. Boudreaux
We give a proof that every space of weighted square-integrable holomorphic functions admits an equivalent weight whose Bergman kernel has zeroes. Here the weights are equivalent in…