Related papers: Lelong-Skoda transform for compact Kaehler manifol…

Let $(Z,\omega)$ be a connected Kahler manifold with an holomorphic action of the complex reductive Lie group $U^{\mathbb C}$, where $U$ is a compact connected Lie group acting in a hamiltonian fashion. Let $G$ be a closed compatible Lie…

We develop a parabolic pluripotential theory on compact K{\"a}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{\`e}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor…

Through the study of some elliptic and parabolic fully nonlinear PDEs, we establish conformal versions of quermassintegral inequality, the Sobolev inequality and the Moser-Trudinger inequality for the geometric quantities associated to the…

A locally conformally K\"ahler (LCK) manifold $M$ is one which is covered by a K\"ahler manifold $\tilde M$ with the deck transform group acting conformally on $\tilde M$. If $M$ admits a holomorphic flow, acting on $\tilde M$ conformally,…

This paper is intended as the first step of a programme aiming to prove in the long run the long-conjectured closedness under holomorphic deformations of compact complex manifolds that are bimeromorphically equivalent to compact K\"ahler…

In this article we are mainly concerned with three dimensional compact K\"ahler spaces with log terminal singularities. We establish the orbifold version of the Bogomolov-Gieseker inequality for stable $\mathbb Q$-sheaves.

Let X be a compact Kahler manifold and let T be a foliated cycle directed by a transversally Lipschitz lamination on X . We prove that the self-intersection of the cohomology class of T vanishes as long as T does not contain currents of…

In this paper, we introduce Steklov and Neumann isocapacitary constants for the $p$-Laplacian on compact manifolds. These constants yield two-sided bounds for the $(p,\alpha)$-Sobolev constants, which degenerate to upper and lower bounds…

We show that the auto-Backlund transformations of the sine-Gordon, Korteweg-deVries, nonlinear Schrodinger, and Ernst equations are related to their respective CPT symmetries. This is shown by applying the CPT symmetries of these equations…

In this note we prove the following result: There is a positive constant $\epsilon(n,\Lambda)$ such that if $M^n$ is a simply connected compact K$\ddot{a}$hler manifold with sectional curvature bounded from above by $\Lambda$, diameter…

We prove an upper bound for the volume of maximal analytic sets on which the generic Lelong number of a closed positive current is positive. As a particular case, we give a uniform upper bound on the volume of the singular locus of an…

For every closed subset $X$ of a stratifiable [resp. metrizable] space $Y$ we construct a positive linear extension operator $T:R^{X\times X}\to R^{Y\times Y}$ preserving constant functions, bounded functions, continuous functions,…

We examine here the space of conformally compact metrics $g$ on the interior of a compact manifold with boundary which have the property that the $k^{th}$ elementary symmetric function of the Schouten tensor $A_g$ is constant. When $k=1$…

We prove that for every compact K\"ahler manifold $X$ there exists an $L$-infinity morphism, lifting the usual cup product in cohomology, from the Kodaira-Spencer differential graded Lie algebra to the suspension of the space of linear…

We use intersection theory techniques to define an invariant of closed 3-manifolds counting the characters of irreducible representations of the fundamental group in PSL(2,C). We note several properties of the invariant and compute the…

We construct examples of hyperKahler manifolds of Picard number two with automorphisms of positive entropy via derived automorphisms of K3 surfaces of Picard number one. Our hyperKahler manifolds are constructed as moduli spaces of…

Let U be a pseudoconvex open set in a complex manifold M. When is U a Stein manifold? There are classical counter examples due to Grauert, even when U has real-analytic boundary or has strictly pseudoconvex points. We give new criteria for…

The aim of this paper is to classify compact, simply connected K\"ahler manifolds which admit J-invariant Killing tensor with two eigenvalues of multiplicity 2 and n-2 and with constant eigenvalue corresponding to 2-dimensional…

For a compact surface $S$ with constant negative curvature $-\kappa$ (for some $\kappa>0$) and genus $g\geq2$, we show that the tails of the distribution of $i(\alpha,\beta)/l(\alpha)l(\beta)$ (where $i(\alpha,\beta)$ is the intersection…

Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for any positive integer n. Under the assumption that T is…