Related papers: Regularization of currents and entropy

Let f be a holomorphic automorphism of a compact Kahler manifold (X,\omega) of dimension k>1. We study the convex cones of positive closed (p,p)-currents T_p, which satisfy a functional relation $f^*(T_p)=\lambda T_p, \lambda>1,$ and some…

Given a closed positive current T on a compact Kahler manifold X, we introduce the notion of non-pluripolar product relative to T of closed positive (1,1)-currents. We recover the well-known non-pluripolar product when T is the current of…

We introduce a notion of super-potential (canonical function) associated to positive closed (p,p)-currents on compact Kaehler manifolds and we develop a calculus on such currents. One of the key points in our study is the use of…

In this work, we introduce the notion of entropy at infinity, and define a wide class of noncompact manifolds with negative curvature, those which admit a critical gap between entropy at infinity and topological entropy. We call them…

We introduce, on a complex Kahler manifold (M,\omega), a notion of energy for harmonic currents of bidegree (1,1). This allows us to define $\int T \wedge T \wedge \omega^{k-2},$ for positive harmonic currents. We then show that for a…

Let $X$ be a compact Kaehler manifold of dimension $k$ and $T$ be a positive closed current on $X$ of bidimension $(p,p)$ ($1\leq p < k-1$). We construct a continuous linear transform $\mathcal{L}_p(T)$ of $T$ which is a positive closed…

We prove that if a positive closed current is bounded by another one with bounded, continuous or Hoelder continuous super-potentials, then it inherits the same property. There are two different methods to define wedge-products of positive…

Let $X$ be a compact K\"ahler manifold of dimension $n.$ Let $T$ and $S$ be two positive closed currents on $X$ of bidegree $(p,p)$ and $(q,q)$ respectively with $p+q\le n.$ Assume that $T$ has a continuous super-potential. We prove that…

We study density currents associated with a collection of positive closed (1,1)-currents. We prove that the density current is unique and determined by the usual wedge product in some classical situations including the case where the…

Let S be a Pfaff system of dimension 1, on a compact complex manifold M. We prove that there is a positive ddbar-closed current T of mass 1 directed by the Pfaff system S. There is no integrability assumption. We also show that local…

Let $X$ be a compact K\"ahler manifold. We study plurisupported currents on $X$, i.e. closed, positive $(1,1)$-currents which are supported on a pluripolar set. In particular, we are able present a technical generalization of…

Let $f:X\to X$ be a dominating meromorphic map of a compact K\"ahler surface of large topological degree. Let $S$ be a positive closed current on $X$ of bidegree $(1,1)$. We consider an ergodic measure $\nu$ of large entropy supported by…

Let $Y$ be a compact K\"ahler manifold. We show that the weak regularization $K_n$ of Dinh and Sibony for the diagonal $\Delta_Y$ (see Section 2 for more detail) is compatible with wedge product in the following sense: If $T$ is a positive…

Extending our results in "Entropy conjecture for continuous maps of nilmanifolds", to appear in Israel Jour. of Math., we confirm that Entropy Conjecture holds for every continuous self-map of a compact $K(\pi,1)$ manifold with the…

In this paper, we prove that for a given surjective holomorphic endomorphism $f$ of a compact K\"ahler manifold $X$ and for some integer $p$ with $1\le p\le k$, there exists a proper invariant analytic subset $E$ for $f$ such that if $S$ is…

We compare the notion of relative non-pluripolar products and that of density currents on compact Kahler manifolds.

We study limiting distribution of the sequence of pull-backs of smooth $(1,1)$ forms and positive closed currents by meromorphic self-maps of compact K\"ahler manifolds.

Let $X$ be a compact complex, not necessarily K\"ahler, manifold of dimension $n$. We characterise the volume of any holomorphic line bundle $L\to X$ as the supremum of the Monge-Amp\`ere masses $\int_X T_{ac}^n$ over all closed positive…

On a class of compact Hermitian manifolds including compact K\"{a}hler manifolds, we prove that the the relative non-pluripolar product is always well-defined. We also prove the monotonicity of the relative non-pluripolar product in terms…

We consider the dynamics of a meromorphic map on a compact kahler surface whose topological degree is smaller than its first dynamical degree. The latter quantity is the exponential rate at which its iterates expand the cohomology class of…