R. Shafikov

activity

20242026

collaborators

4 papers

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.CV2025

Levi-flats in $CP^{n}$ : a survey for nonexperts

Rasul Shafikov

This survey paper, aimed at nonexperts in the field, explores various proofs of nonexistence of real analytic Levi-flat hypersurfaces in $C P^{n}$ , $n > 2$ . Some generalizations…

math.CV2025

Polynomially convex embeddings and CR singularities of real manifolds

Purvi Gupta, Rasul Shafikov

It is proved that any smooth manifold $M$ of dimension $m$ admits a smooth polynomially convex embedding into $C^{n}$ when $n \geq ⌊ 5 m /4 ⌋$ . Further, such…

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…

Meromorphic Convexity on Complex Manifolds

Levi-flats in CPn: a survey for nonexperts

Polynomially convex embeddings and CR singularities of real manifolds

Hypersurface Convexity and Extension of KÃ¤hler Forms

Levi-flats in $CP^{n}$ : a survey for nonexperts