arXiv subjects
Publications and source records attributed to Octavian Mitrea.
Let $S$ be a smooth, totally real, compact immersion in $\mathbb{C}^n$ of real dimension $m \leq n$, which is locally polynomially convex and it has finitely many points where it self-intersects finitely many times, transversely or non-transversely. We prove that $S$ is rationally convex if and only if it is isotropic with respect to a "degenerate" Kähler form in $\mathbb{C}^n$.
The usual notion of set-convexity, valid in the classical Euclidean context, metamorphoses into several distinct convexity types in the more general Riemannian setting. By studying this phenomenon in reverse, we characterize complete manifolds for which certain convexity types are assumed a priori to coincide.
It is proved that any smooth open Whitney umbrella in $\mathbb C^2$ is locally polynomially convex near the singular point.