Related papers: Rudin's Theorem and Projective Hulls

The notion of the projective hull of a compact set in a complex projective space was introduced by Harvey and Lawson in 2006. In this paper we describe the projective hull by Poletsky sequences of analytic discs, in analogy to the known…

We introduce the notion of a ``projective hull'' for subsets of complex projective varieties, parallel to the idea of the polynomial hull in affine varieties. With this concept, a generalization of J. Wermer's classical theorem on the hull…

Using a recent result of L\'arusson and Poletsky regarding plurisubharmonic subextensions we prove a disc formula for the quasiplurisubharmonic global extremal function for domains in complex projective space. As a corollary we get a…

Let X be a complex manifold and c a simple closed curve in X. We address the question: What conditions on c ensure the existence of a 1-dimensional complex subvariety V with boundary c in X. When X = C^n, an answer to this question involves…

In this expository paper we collect many recent advances in analytic function spaces of several complex variables related with trace problem. We consider various function space of analytic functions of several variables in various domains…

We investigate a specific infinite urn scheme first considered by Karlin (1967). We prove functional central limit theorems for the total number of urns with at least k balls for different k.

In this expository paper we collect many recent advances in analytic function spaces of several complex variables related with trace problem in tubular domains over symmetric cones and bounded strongly pseudoconvex domains with smooth…

In 1927 Littlewood constructed an example of bounded holomorphic function on the unit disk, which diverges almost everywhere along rotated copies of any given curve in the unit disk ending tangentially to the boundary. This theorem was the…

We will show that a theorem of Rudin \cite{wr1}, \cite{wr}, permits us to determine minimal projections not only with respect to the operator norm but with respect to quasi-norms in operators ideals and numerical radius in many concrete…

A new elementary proof for a theorem of D. Burns and S. Krantz on the rigidity of the analytic self maps of the unit disc was recently discovered by L. Baracco, D. Zaitsev, and G. Zampieri. We use their argument to generalize Burns-Krantz…

Let P be a locally finite disk pattern on the complex plane C whose combinatorics are described by the one-skeleton G of a triangulation of the open topological disk and whose dihedral angles are equal to a function \Theta:E\to [0,\pi/2] on…

We prove that if $K$ is a compact subset of an affine variety O = P^n - D (where D is a projective hypersuface), and if K is a compact subset of a closed analytic subvariety V \subset O, then the projective hull K^ of K has the property…

M. E. Rudin in "Partial orders on the types of $\beta {N}$", (Trans. Amer. Math. Soc., 155, 1971, 353-362) proved (under CH) that for each P-point $u$ there is a P-point $v$ such that $v>_{RK}u$. A. Blass in "Rudin - Kisler ordering on…

We prove that every polytope described by algebraic coordinates is the face of a projectively unique polytope. This provides a universality property for projectively unique polytopes. Using a closely related result of Below, we construct a…

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…

We analyze the behavior of polarized complex variations of Hodge structure on the punctured unit disk. For integral variations of Hodge structure, this analysis was first carried out by Wilfried Schmid. We get rid of the assumption that the…

The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set $S \subset \mathbb{R}^d$, then there are at most $2d$ points of $S$ whose convex hull contains the origin in the interior.…

We consider complex projective space P^{n} and a smooth closed curve gamma in P^{n}. Harvey and Lawson have defined the notion of the projective hull \hat{K} of a compact subset K in P^n. This concept is an analogue of the polynomial hull…

We prove two-sided bounds on the expected values of several geometric functionals of the convex hull of Brownian motion in $\mathbb{R}^n$ and their inverse processes. This extends some recent results of McRedmond and Xu (2017),…

Rudin conjectured that there are never more than c N^(1/2) squares in an arithmetic progression of length N. Motivated by this surprisingly difficult problem we formulate more than twenty conjectures in harmonic analysis, analytic number…