Related papers: On Tangential and Projectively Adjacent Approach R…

We prove local connectivity of the boundaries of invariant simply connected attracting basins for a class of transcendental meromorphic maps. The maps within this class need not be geometrically finite or in class $\mathcal B$, and the…

In this paper we will deal with problems in approximation theory of bounded analytic functions on the unit disc and their boundary behavior on the unit circle. We will attempt to unify two known such theorems to create a stronger theorem.…

Solving the Plateau problem means to find the surface with minimal area among all surfaces with a given boundary. Part of the problem actually consists of giving a suitable definition to the notions of 'surface', 'area' and 'boundary'. In…

Exponential convergence type results are proved for holomorphic curves in the symplectization of a contact manifold $Y$ with boundary on a Legendrian cylinder. The results are proven in all dimensions, and generalize earlier work specific…

We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…

In this note, we construct examples of bounded smooth convex domains with no non-trivial analytic discs on the boundary which possess a holomorphic self-map without fixed points so that the iterates do not converge to a point (that is, the…

Raynaud and Gruson showed that there is a reasonable algebro-geometric notion of family of discrete (infinite-dimensional) vector spaces. The author introduces a notion of family of Tate spaces ("Tate" means "locally linearly compact") and…

This article concerns linear parts of minimal resolutions of finitely generated modules over commutative local, or graded rings. The focus is on the linearity defect of a module, which marks the point after which the linear part of its…

For every vector $\overline \alpha\in \RR^n$ and for every rational approximation $(\overline p,q)\in \RR^n\times\RR$ we can associate the displacement vector $q\alpha-\overline p$. We focus on algebraic vectors, namely $\overline…

Suppose that $A$ and $B$ are closed subsets of a Euclidean space such that $A\cap B\neq\varnothing$, and we aim to find a point in this intersection with the help of the sequences $(a_n)_\nnn$ and $(b_n)_\nnn$ generated by the \emph{method…

We prove a version of Gromov's compactness theorem for pseudo-holomorphic curves which holds locally in the target symplectic manifold. This result applies to sequences of curves with an unbounded number of free boundary components, and in…

The log-concave projection is an operator that maps a d-dimensional distribution P to an approximating log-concave density. Prior work by D{\"u}mbgen et al. (2011) establishes that, with suitable metrics on the underlying spaces, this…

We consider, in a first instance, the class of boundaries of sets with locally finite perimeter whose (weakly defined) mean curvature is $g \nu$, for a given continuous positive ambient function $g$, and where $\nu$ denotes the inner…

A topological space is locally equiconnected if there exists a neighborhood $U$ of the diagonal in $X\times X$ and a continuous map $\lambda:U\times[0,1]\to X$ such that $\lambda(x,y,0)=x$, $\lambda(x,y,1)=y$ et $\lambda(x,x,t)=x$ for…

We investigate the family of surfaces defined by the affine equation $$Y^2 + Z^2 = (aT^2 + b)(cT^2 +d)$$ where $\vert ad-bc \vert=1$ and develop an asymptotic formula for the frequency of Hasse principle failures. We show that a positive…

Let f be a germ of an analytic function at infinity that can be analytically continued along any path in the complex plane deprived of a finite set of points, f \in\mathcal{A}(\bar{\C} \setminus A), \sharp A <\infty. J. Nuttall has put…

Here is an English summary of the abstract: This research investigates a geometric dynamical mechanism within a specific class of domains that contain a fixed convex core. By using a radial structure that links the boundaries of the core…

We show that an earlier conjecture of the author, on diophantine approximation of rational points on varieties, implies the ``abc conjecture'' of Masser and Oesterl'e. In fact, a weak form of the former conjecture is sufficient, involving…

Motivated by limits of critical inhomogeneous random graphs, we construct a family of sequences of measured metric spaces that we call continuous multiplicative graphs, that are expected to be the universal limit of graphs related to the…

In a paper from 1960, Felix Browder established a theorem concerning the continuation of the fixed points of a family of continuous functions $f_t:X\to X$ depending continuously on a parameter $t\in [0,1]$, where $X$ is a convex and compact…