# Totally real embeddings with prescribed polynomial hulls

@article{Arosio2019TotallyRE,
title={Totally real embeddings with prescribed polynomial hulls},
author={Leandro Arosio and Erlend Fornaess Wold},
journal={Indiana University Mathematics Journal},
year={2019}
}
• Published 3 February 2017
• Mathematics
• Indiana University Mathematics Journal
We embed compact $C^\infty$ manifolds into $\mathbb C^n$ as totally real manifolds with prescribed polynomial hulls. As a consequence we show that any compact $C^\infty$ manifold of dimension $d$ admits a totally real embedding into $\mathbb C^{\lfloor \frac{3d}{2}\rfloor}$ with non-trivial polynomial hull without complex structure.

### Polynomially convex embeddings of even-dimensional compact manifolds

• Mathematics
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
• 2020
We show that, for $k>1$, any $2k$-dimensional compact submanifold of $\mathbb{C}^{3k-1}$ can be perturbed to be polynomially convex and totally real except at a finite number of points. This lowers

### odd-dimensional closed

• Mathematics
• 2022
Given a closed orientable abstract manifold M of odd dimension 2k +1, k ≥ 2, it is natural to look for the least n such that M can be embedded in C with certain prescribed properties. We recall that

### Polynomial hulls of arcs and curves

It is shown that there exist arcs and simple closed curves in C 3 \mathbb {C}^3 with nontrivial polynomial hulls that contain no analytic discs. It is also shown that in any

### The convergence of hulls of curves

• Mathematics
Mathematische Zeitschrift
• 2022
We prove results about limits of simple closed curves and polynomial hulls. The results show, in particular, that the polynomially convex, rectifiable simple closed curves in Cn, n ≥ 2, form a dense

### C V ] 2 1 D ec 2 01 9 POLYNOMIAL HULLS OF ARCS AND CURVES

It is shown that there exist arcs and simple closed curves in C with nontrivial polynomial hulls that contain no analytic discs. It is also shown that in any bounded Runge domain of holomorphy in C

### Achievements and evaluation

• Mathematics
• 2018
In the field of complex dynamics, the problem of classifying Fatou components for various classes of holomorphic maps is a major challenging open problem. It has been known that any non-recurrent

### No topological condition implies equality of polynomial and rational hulls

• Alexander J. Izzo
• Computer Science
Proceedings of the American Mathematical Society
• 2019
It is shown that no purely topological condition implies the equality of the polynomial and rational hulls of a set: for any uncountable, compact subset of a Euclidean space, there exists a set that is rationally convex but not polynomially convex.

### Polynomially convex embeddings of odd-dimensional closed manifolds

• Mathematics
• 2020
Abstract It is shown that any smooth closed orientable manifold of dimension 2⁢k+1{2k+1}, k≥2{k\geq 2}, admits a smooth polynomially convex embedding into ℂ3⁢k{\mathbb{C}^{3k}}. This improves by 1

## References

SHOWING 1-10 OF 12 REFERENCES

### Hulls of Surfaces

• Mathematics
• 2015
In this paper it is shown that every compact two-dimensional manifold $S$, with or without boundary, can be embedded in $\mathbb C^3$ as a smooth submanifold $\Sigma$ in such a way that the

### Optimality for totally real immersions and independent mappings of manifolds into C^N

• Mathematics
• 2012
The optimal target dimensions are determined for totally real immersions and for independent mappings into complex affine spaces. Our arguments are similar to those given by Forster, but we use

### Holomorphic convexity and Carleman approximation by entire functions on Stein manifolds

• Mathematics
• 2011
We give necessary and sufficient conditions for totally real sets in Stein manifolds to admit Carleman approximation of class $${\mathcal C^k}$$, k ≥ 1, by entire functions.

### Presence or absence of analytic structure in maximal ideal spaces

• Mathematics
• 2016
We study extensions of Wermer’s maximality theorem to several complex variables. We exhibit various smoothly embedded manifolds in complex Euclidean space whose hulls are non-trivial but contain no

### Approximation by automorphisms on smooth submanifolds of Cn

We denote by AutC n the group of all holomorphic automorphisms of the complex Euclidean space C". This is a very large and complicated group when n > 2; tbr results in this direction see [5, 6, 11,

### Approximation of biholomorphic mappings by automorphisms of Cn

• Mathematics
• 1993
In this paper we prove several results on approximation of biholomorphic mappings between domains in C" (n _>-2) by holomorphic automorphisms of C". Recall that the group of holomorphic automorphisms

### Hulls of subsets of the torus in C2

© Annales de l’institut Fourier, 1998, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions

### Polynomial convexity and totally real manifolds

• Mathematics
• 2009
In this article we study generic properties of totally real submanifolds M of . On the one hand we show that if M is polynomially convex and also has bounded exhaustion hulls, then sufficiently small

### Differential Topology, Graduate Texts

• in Mathematics
• 1976