Related papers: A Runge approximation theorem for pseudo-holomorph…

The purpose of this paper is to study holomorphic approximation and approximation of $\bar\partial$-closed forms in complex manifolds of complex dimension $n\geq 1$. We consider extensions of the classical Runge theorem and the Mergelyan…

We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…

We present a geometric proof of the theorem saying that holomorphic maps from Runge domains to affine algebraic varieties admit approximation by Nash maps. Next we generalize this theorem.

We prove that the classical Oka property of a complex manifold Y, concerning the existence and homotopy classification of holomorphic mappings from Stein manifolds to Y, is equivalent to a Runge approximation property for holomorphic maps…

We show that biholomorphic maps between certain pairs of Runge domains in the complex affine space $\mathbb C^n$, $n>1$, are limits of holomorphic automorphisms of $\mathbb C^n$. A similar result holds for volume preserving maps and also in…

A compact subset $K$ of the complex plane $\C$ is a set of polynomial (respectively rational) approximation if $P(K)=A(K)$ (respectively $R(K)=A(K)$), where $P(K)$ (respectively $R(K)$) is the family of functions on $K$ which are uniform…

We approximate smooth maps defined on non-compact totally real manifolds by holomorphic automorphisms of $\mathbb C^n$.

The purpose of this article is to show a second main theorem with the explicit truncation level for holomorphic mappings of $ \mathbb{C} $ (or of a compact Riemann surface) into a compact complex manifold sharing divisors in subgeneral…

This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…

The purpose of this paper is to generalize a theorem of Segal from [Seg79] proving that the space of holomorphic maps from a Riemann surface to a complex projective space is homology equivalent to the corresponding space of continuous maps…

It is known from the Runge approximation theorem that every function which is holomorphic in a neighborhood of a compact polynomially convex set $K\subset \complexes^{n}$ can be approximated uniformly on $K$ by analytic polynomials. We…

We establish universal approximation theorems for infinite-dimensional geometric rough paths, i.e., we show that continuous functions on the space of infinite-dimensional weakly geometric H\"older continuous rough paths can be approximated…

Let D be a domain in C^n with smooth boundary, of finite 1-type at a point p in the boundary and such that the closure of D has a basis of Stein Runge neighborhoods. Assume that there exists an analytic disc which intersects the closure of…

We prove that holomorphic maps from an open subset of a complex smooth projective curve to a complex smooth projective rationally simply connected variety can be approximated by algebraic maps for the compact-open topology. This theorem can…

In this paper we obtain a Carleman approximation theorem for maps from Stein manifolds to Oka manifolds. More precisely, we show that under suitable complex analytic conditions on a totally real set $ M $ of a Stein manifold $X$, every…

In this paper we survey the theory of holomorphic approximation, from the classical 19th century results of Runge and Weierstrass, continuing with the 20th century work of Oka and Weil, Mergelyan, Vitushkin and others, to the most recent…

Let $K$ be a closed polydisc or ball in $\C^n$, and let $Y$ be a quasi projective algebraic manifold which is Zariski locally equivalent to $\C^p$, or a complement of an algebraic subvariety of codimension $\ge 2$ in such manifold. If $r$…

We consider a smooth CR mapping $f$ from a real-analytic generic submanifold $M$ in $\bC^N$ into $\bC^N$. For $M$ of finite type and essentially finite at a point $p\in M$, and $f$ formally finite at $p$, we give a necessary and sufficient…

Let X be a compact (resp. compact and nonsingular) real algebraic variety and let Y be a homogeneous space for some linear real algebraic group. We prove that a continuous (resp. C^infinity) map f:X-->Y can be approximated by regular maps…

In this paper, we give an estimate of sub-Laplacian of Riemannian distance functions in pseudo-Hermitian geometry which plays a similar role as Laplacian comparison theorem in Riemannian geometry, and deduce a prior horizontal gradient…