Related papers: Classification of Half Planar Maps

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

An operator convex function on (0,\infty) which satisfies the symmetry condition k(1/x) = x k(x) can be used to define a type of non-commutative multiplication by a positive definite matrix (or its inverse) using the primitive concepts of…

We study learning of indexed families from positive data where a learner can freely choose a hypothesis space (with uniformly decidable membership) comprising at least the languages to be learned. This abstracts a very universal learning…

The existence of translated curves for quasiperiodically forced maps is established, under very mild regularity hypotheses, for rotation numbers of constant type. Among the translated curves, the invariant curves are characterized as the…

We consider perturbations of quadratic maps $f_a$ admitting an absolutely continuous invariant probability measure, where $a$ is in a certain positive measure set $\mathcal{A}$ of parameters, and show that in any neighborhood of any such an…

The aim of this note is to discuss in more detail the Pohozaev-type identities that have been recently obtained by the author, Paul Laurain and Tristan Rivi\`ere in the framework of half-harmonic maps defined either on $R$ or on the sphere…

It is shown that if a proper holomorphic map $f: \mathbb C^n \to \mathbb C^N$, $1<n\le N$, sends a pseudoconvex real analytic hypersurface of finite type into another such hypersurface, then any $n-1$ dimensional component of the critical…

In a recent paper~\cite{DDL10} we studied basic properties of partial immersions and partially free maps, a generalization of free maps introduced first by Gromov in~\cite{Gro70}. In this short note we show how to build partially free maps…

For a fixed marked surface $S$, we show that the problem of deciding whether or not a mapping class is reducible lies in $\textbf{NP}$. As usual this immediately gives an exponential time algorithm to decide whether or not a mapping class…

For any abstract subfactor planar algebra $P$, there exists a finite index extremal subfactor $M_0 \subset M_1$ with $P$ as its standard invariant. In this paper, we classify the automorphism group of a bipartite graph planar algebra, and…

The trichotomy between regular, semiregular, and strongly irregular boundary points for $p$-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality,…

By using a similar pattern of arguments, we show that in three categories the collection of isomorphisms forms a residual subset of the space of morphisms. We first consider surjective continuous mappings on Cantor spaces. Next, we look at…

Given a hypersurface in the complex projective $n$-space we prove several known formulas for the degree of its polar map by purely algebro-geometric methods. Furthermore, we give formulas for the degree of its polar map in terms of the…

Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…

We establish new characterizations of graphs belonging to the $\mathbf{W}_p$ class. In addition, we characterize locally triangle-free $\alpha$-critical graphs in this class. As a consequence, our results yield a partial answer to a…

A surface M is called p-minimal if one of the coordinate functions is p-harmonic in the inner metric. We show that in the twodimensional case the Gaussian map of such surfaces is quasiconformal. In the case when the surface is a tube we…

Locally stable maps $S^3\to\mathbb{R}^4$ are classified up to homotopy through locally stable maps. The equivalence class of a map $f$ is determined by three invariants: the isotopy class $\sigma(f)$ of its framed singularity link, the…

A regular map is a surface together with an embedded graph, having properties similar to those of the surface and graph of a platonic solid. We analyze regular maps with reflection symmetry and a graph of density strictly exceeding 1/2, and…

Consider the (formal/analytic/algebraic) map-germs Maps(X,(k^p,o)). Let G be the group of right/contact/left-right transformations. I extend the following (classical) results from the real/complex-analytic case to the case of arbitrary…

Completely positive trace preserving maps are widely used in quantum information theory. These are mostly studied using the master equation perspective. A central part in this theory is to study whether a given system of dynamical maps…