7 problems

Let $M$subset ${\mathcal M}$ be a smooth real submanifold of a Stein manifold ${\mathcal M}$, and let $p$ be an elliptic CR singular point of $M$. Denote by $\widehat{M}$ the local…

Second conjecture. The disc $K$ is polynomially convex if

First conjecture. Any totally real disc lying in a nonsingular Levi-flat hypersurface in $\mathbb{C}^2$ is polynomially convex.

Let a codimension-one holomorphic foliation on $\mathbb{C}\mathbb{P}^2$ be allowed to have singularities, and let a leaf be a leaf of this foliation. Leaf-accumulation conjecture.…

A Levi-flat hypersurface is a real-analytic hypersurface whose CR distribution is integrable. A hyperbolic torus bundle is a bundle with toric fiber…

A Levi-flat hypersurface is a real-analytic hypersurface whose CR distribution is integrable, and a hyperbolic torus bundle over the circle is a bundle with fiber…

Let $\mathbb{T}_{n}=\mathbb{C}^{n}/\Gamma$ be a complex torus, let $\pi:\mathbb{C}^{n}\to\mathbb{T}_{n}$ be the canonical projection, and let $M$ be a compact Levi flat hypersurfac…