Related papers: Transcendental holomorphic maps between real algeb…
We give conditions for topological and bi-Lipschitz equivalences within a class of mixed singularities of Pham-Brieskorn type. As a consequence, we construct infinite families that are topologically trivial but have distinct bi-Lipschitz…
We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollaries 2.3, 2.4, and 2.6), biharmonic maps between…
In semialgebraic geometry, projections play a prominent role. A definable choice is a semialgebraic selection of one point in every fiber of a projection. Definable choices exist by semialgebraic triviality, but their complexity depends…
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…
Using the theory of exterior differential systems, we study the existence of germ of pseudo-holomorphic disk in a real analytic hypersurface locally defined in a complex manifold equipped with J a real analytic almost complex structure. The…
We study invariants coming from certain optimisation problems for nef divisors on surfaces. These optimisation problems arise in work of the author and collaborators tying obstructions to embeddings between symplectic 4-manifolds to…
Let X be a real algebraic surface. The comparison between the volume of real and complex loci of ample divisors D brings us to define the concordance, which is a number between 0 and 1. This number equals 1 when the Picard number is 1, and…
We study smooth rational closed embeddings of the real affine line into the real affine plane, that is algebraic rational maps from the real affine line to the real affine plane which induce smooth closed embeddings of the real euclidean…
In this paper \emph{analytic equivalence} of geometric transition is defined in such a way that equivalence classes of geometric transitions turn out to be the \emph{arrows} of the \cy web. Then it seems natural and useful, both from the…
We give a survey about the Runge approximation problem for a holomorphic function defined on the unit ball of a complex Banach space.
We study a germ of real analytic n-dimensional submanifold of C n that has a complex tangent space of maximal dimension at a CR singularity. Under some assumptions , we show its equivalence to a normal form under a local biholomorphism at…
Algebraically constructible functions connect real algebra with the topology of algebraic sets. In this survey we present some history, definitions, properties, and algebraic characterizations of algebraically constructible functions, and a…
We study various classes of real hypersurfaces that are not embeddable into more special hypersurfaces in higher dimension, such as spheres, real algebraic compact strongly pseudoconvex hypersurfaces or compact pseudoconvex hypersurfaces of…
A necessary and sufficient condition for an operator space to support a multiplication making it completely isometric and isomorphic to a unital operator algebra is proved. The condition involves only the holomorphic structure of the Banach…
Given a Banach space X and a subspace Y, the pair (X,Y) is said to have the approximation property (AP) provided there is a net of finite rank bounded linear operators on X all of which leave the subspace Y invariant such that the net…
We show that a pseudo-holomorphic embedding of an almost-complex $2n$-manifold into almost-complex $(2n + 2)$-Euclidean space exists if and only if there is a CR regular embedding of the $2n$-manifold into complex $(n + 1)$-space. We remark…
We prove a symmetric version of B\'ezout's theorem. More precisely, we show that the symmetric orbit type of a transverse intersection of complex symmetric hypersurfaces in projective space is determined by the degrees. In the projective…
Lying at the intersection of Ado's theorem and the Nash embedding theorem, we consider the problem of finding faithful representations of Lie groups which are simultaneously isometric embeddings. Such special maps are found for a certain…
multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on $L^2$ spaces of functions are never compact and then such…
Real smooth three-dimensional or higher Banach spaces are isomorphic with respect to the nonlinear structure of Birkhoff-James orthogonality if and only if they are isometrically isomorphic. Moreover, using smooth Radon planes and…