Related papers: An extension theorem for K\"ahler currents

We generalize Rado's extension theorem to complex spaces.

We compute the moduli Kahler potential for M-theory on a compact manifold of G_2 holonomy in a large radius approximation. Our method relies on an explicit G_2 structure with small torsion, its periods and the calculation of the approximate…

We give a numerical characterization of the Kahler cone of a possibly singular compact analytic variety which is embedded in a smooth ambient space.

We prove that on compact K\"ahler manifolds solutions to the complex Monge-Amp\`ere equation, with the the right hand side in $L^p, p>1,$ are H\"older continuous.

We establish the convexity of Mabuchi's K-energy functional along weak geodesics in the space of Kahler potentials on a compact Kahler manifold thus confirming a conjecture of Chen and give some applications in Kahler geometry, including a…

We present an inductive strategy to show the existence of rational curves on compact Kaehler manifolds which are not minimal models but have a pseudoeffective canonical bundle. The tool for this inductive strategy is a weak subadjunction…

The notion of an exterior differential system (on a manifold) has recently been extended to the setting of a Lie algebroid. Here, we further develop the theory and we present two versions of the Cartan-K\"ahler theorem in the case where the…

We study many properties concerning weak K\"ahlerianity on compact complex manifolds which admits a holomorphic submersion onto a K\"ahler or a balanced manifold. We get generalizations of some results of Harvey and Lawson (the K\"ahler…

It is proved that solutions of the complex Monge-Amp\`ere equation on compact K\"ahler manifolds with right hand side in $L^p, p>1$ are uniformly H\"older continuous under the assumption on non-negative orthogonal bisectional curvature.

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…

Let $D_j\subset\Bbb C^{k_j}$ be a pseudoconvex domain and let $A_j\subset D_j$ be a locally pluripolar set, $j=1,...,N$. Put$$X:=\bigcup_{j=1}^N A_1\times...\times A_{j-1}\times D_j\times A_{j+1}\times...\times A_N\subset\Bbb…

We develop an alternative approach to Degenerate complex Monge-Amp\`ere equations on compact K\"ahler manifolds based on the concept of viscosity solutions and compare systematically viscosity concepts with pluripotential theoretic ones. We…

We study continuity properties of generalized Monge-Amp\`ere operators for plurisubharmonic functions with analytic singularities. In particular, we prove continuity for a natural class of decreasing approximating sequences. We also prove a…

In this paper, we prove that a compact K\"ahler manifold $X$ with pseudo-effective (resp. singular positively curved) tangent bundle admits a smooth (resp. locally constant) rationally connected fibration $\phi \colon X \to Y$ onto a finite…

In this paper, we give a criterion for the properness of the K-energy in a general Kahler class of a compact Kahler manifold by using Song-Weinkove's result. As applications, we give some Kahler classes on…

In a previous paper, we presented an Abstract Beurling's Theorem for valuation Hilbert modules over valuation algebras. In this paper, we shall apply this theorem to obtain complete descriptions of the closed invariant subspaces of a number…

We survey some recent developments on solutions of the K\"ahler-Ricci flow on compact K\"ahler manifolds which exist for all positive times.

A complex Monge-Amp\`ere equation for differential $(p,p)$-forms is introduced on compact K\"ahler manifolds. For any $1 \leq p < n$, we show the existence of smooth solutions unique up to adding constants. For $p=1$, this corresponds to…

Theorem (uniformization). Let X be a compact Kahler manifold of dimension n with large, residually finite and nonamenable fundamental group. Then its universal covering is a bounded domain in the n-dimensional affine space.

We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.