Totally real embeddings with prescribed polynomial hulls

Discs in hulls of real immersions to Stein manifolds

We obtain results on the existence of complex discs in plurisubharmonically convex hulls of Lagrangian and totally real immersions to Stein manifolds.

Polynomially convex hulls of singular real manifolds

We obtain local and global results on polynomially convex hulls of Lagrangian and totally real submanifolds of $C^n$ with self-intersections and open Whitney umbrella points.

Riemann surfaces and totally real tori

Given a generic totally real torus unknotted in the unit sphere of the complex plane, we prove the following alternative : either there exists a filling of the torus by holomorphic discs and the torus is rationally convex, or its rational hull contains a holomorphic annulus.

The Rational Hull of Rudin's Klein Bottle

In this note, a general result for determining the rational hulls of fibered sets in $\mathbb{C}^2$ is established. We use this to compute the rational hull of Rudin's Klein bottle, the first explicit example of a totally real nonorientable surface in $\mathbb{C}^2$. In contrast to its polynomial hull, which was shown to contain an open set by the first author in 2012, its rational hull is shown to be two-dimensional. Using the same method, we also compute the rational hulls of some other surfaces in $\mathbb{C}^2$.

紧致三维流形的全纯包

Holomorphic Hulls for Compact 3-Manifolds

研究紧致实三维流形嵌入到C^3中沿复切线的全纯包结构，通过构造嵌入控制Bishop不变量，揭示椭圆、双曲和抛物点的不同局部包性质。

Polynomially Convex Embeddings of Even-Dimensional Compact Manifolds

The totally-real embeddability of any $2k$-dimensional compact manifold $M$ into $\mathbb C^n$, $n\geq 3k$, has several consequences: the genericity of polynomially convex embeddings of $M$ into $\mathbb C^n$, the existence of $n$ smooth generators for the Banach algebra $\mathcal C(M)$, the existence of nonpolynomially convex embeddings with no analytic disks in their hulls, and the existence of special plurisubharmonic defining functions. We show that these results can be recovered even when $n=3k-1$, $k>1$, despite the presence of complex tangencies, thus lowering the known bound for the op…