Related papers: Discs in hulls of real immersions to Stein manifol…
We consider generalizations of rational convexity to Stein manifolds and prove related results
We prove that an immersed lagrangian submanifold in $\C^n$ with quadratic self-tangencies is rationally convex. This generalizes former results for the embedded and the immersed transversal cases.
Following earlier work of Loftin-McIntosh, we study minimal Lagrangian immersions of the universal cover of a closed surface (of genus at least 2) into CH2, with prescribed data of a conformal structure plus a holomorphic cubic…
The largest discs contained in a regular tetrahedron lie in its faces. The proof is closely related to the theorem of Fritz John characterising ellipsoids of maximal volume contained in convex bodies.
We use our disc formula for the Siciak-Zahariuta extremal function to characterize the polynomial hull of a connected compact subset of complex affine space in terms of analytic discs.
In this note, we investigate the relation between double points and complex points of immersed surfaces in almost-complex 4-manifolds and show how estimates for the minimal genus of embedded surfaces lead to inequalities between the number…
In recent years methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this note it is shown that the latter method is actually…
This paper is devoted to the study of the global properties of harmonically immersed Riemann surfaces in $\mathbb{R}^3.$ We focus on the geometry of complete harmonic immersions with quasiconformal Gauss map, and in particular, of those…
In this paper, we study the existence of harmonic and bi-harmonic maps into Riemannian manifolds admitting a conformal vector field, or a nontrivial Ricci solitons.
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
We use nonsmooth critical point theory and the theory of geodesics with obstacle to show a multiplicity result about orthogonal geodesic chords in a Riemannian manifold (with boundary) which is homeomorphic to an $N$-disk. This applies to…
A geometric approach to immersion formulas for soliton surfaces is provided through new cohomologies on spaces of special types of $\mathfrak{g}$-valued differential forms. This leads us to introduce Poincar\'e-type lemmas for these…
Totally real immersions $f$ of a closed real surface $\Sigma$ in an almost complex surface $M$ are completely classified, up to homotopy through totally real immersions, by suitably defined homotopy classes $\frak{M}(f)$ of mappings from…
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 orientable manifolds as far as possible and so…
The paper is a survey of recent results in geometric representation theory describing group actions which induce multiplicity-free representations in the spaces of holomorphic functions. For connected compact Lie groups of automorphisms of…
In this paper, we revise some results on rigidity and vanishing properties obtained by \textit{Cuong et.al} in \cite{CDS24} on $n$-dimensional totally real minimal submanifolds $M$ immersed in complex space forms $\widetilde{M}^n(c)$, for…
We study pseudoholomorphic discs with boundaries attached to a real hypersurface in an almost complex manifold of dimension 2. We prove that if the hypersurface contains no discs, then they fill a one sided neighborhood of the hypersurface.
We establish an $h$-principle for exact Lagrangian immersions with transverse self-intersections and the minimal, or near-minimal number of double points. One corollary of our result is that any orientable closed 3-manifold admits an exact…
We study the existence or not of harmonic diffeomorphisms between certain domains in the Euclidean 2-sphere. In particular, we show harmonic diffeomorphisms from circular domains in the complex plane onto finitely punctured spheres, with at…
Using Legendrian immersions and, in particular, Legendre curves in odd dimensional spheres and anti De Sitter spaces, we provide a method of construction of new examples of Hamiltonian-minimal Lagrangian submanifolds in complex projective…