Local Polynomial Convexity of the Union of two Tangential Totally Real Graphs in $$\mathbb {C}^3$$

A note on polynomial convexity of the union of finitely many totally-real planes in [formula omitted

We consider the following question: Let S 1 and S 2 be two smooth, totally-real surfaces in \({\mathbb{C}^2}\) that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is \({S_1\cup S_2}\) locally polynomially convex at the origin? If T 0 S 1 ∩ T 0 S 2 = {0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When \({dim_\mathbb{R}(T_0S_1\cap T_0S_2)=1}\), we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.

Local polynomial convexity of tangential unions of totally real graphs in C 2

We discuss local polynomial convexity of real analytic Levi-flat hypersurfaces in [Formula: see text], [Formula: see text], near singular points.

Polynomial approximation, local polynomial convexity, and degenerate CR singularities

In this note by using techniques similar to that of [2] and [3], we study the local polynomial convexity of perturbation of union of two totally real planes meeting along a real line.

Local polynomial convexity of graphs of functions in several variables

Local Polynomial Convexity of the Unfolded Whitney Umbrella in ℂ2

Local polynomial convexity of certain graphs in C3