Related papers: A sharp effectiveness result of Demailly's strong …

In this article, stimulated by the effectiveness in Berndtsson's solution of the openness conjecture and continuing our solution of Demailly's strong openness conjecture, we discuss conditions to guarantee the effectiveness of the…

We give a proof of the openness conjecture of Demailly and Koll\'ar.

In this article, we solve the strong openness conjecture on the multiplier ideal sheaves for the plurisubharmonic functions posed by Demailly. We prove two conjectures about the growth of the volumes of the sublevel sets of plurisubharmonic…

We give a proof of the openness conjecture of Demailly and Koll\'ar for positively curved singular metrics on ample line bundles over projective varieties. As a corollary it follows that the openness conjecture for plurisubharmonic…

We discuss recent versions of the Brunn-Minkowski inequality in the complex setting, and use it to prove the openness conjecture of Demailly and Koll\'ar.

In this note, we reveal that our solution of Demailly's strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Koll\'{a}r and Jonsson-Mustat\u{a} implies the truth of twisted…

We reduce the Openness Conjecture of Demailly and Koll\'ar on the singularities of plurisubharmonic functions to a purely algebraic statement.

In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.

In the present article, we obtain an estimation of the weighted $L^2$ norm near the singularities of plurisubharmonic weight related to Demailly's strong openness conjecture, which implies the convergence of the weighted $L^2$ norm.

In this paper, we show the equivalence of the sharp effectiveness results of the strong openness property of multiplier ideal sheaves obtained in \cite{BG1} using $\xi-$Bergman kernels and in \cite{Guan19} using minimal $L^2$ integrals.

This paper presents our proof of the "strong Macdonald constant term conjecture" of P. Hanlon and B. Feigin.

We prove sharp uniqueness results for a wide class of one-dimensional discrete evolutions. The proof is based on a construction from the theory of complex Jacobi matrices combined with growth estimates of entire functions.

This is a survey article, presenting few of the mathematical achievements of J.-P. Demailly. We discuss a few aspects of his approach for Fujita conjecture, and results around the K\"ahler cone of a compact K\"ahler manifold. The article…

We consider strong expansions of the theory of ordered abelian groups. We show that the assumption of strength has a multitude of desirable consequences for the structure of definable sets in such theories, in particular as relates to…

We prove the Demailly--Peternell--Schneider conjecture in positive characteristic: if $X$ is a smooth projective variety over an algebraically closed field of characteristic $p>0$ with $-K_X$ is nef, then the Albanese morphism $a: X \to A$…

We develop tools to prove D\'iaz and Park's sharpness conjecture (see [8]) for fusion systems admitting tame families of fusion subsystems (see Theorem A). We use such tools to prove the conjecture for all Benson-Solomon fusion systems (see…

We prove a sharp integral inequality for the dyadic maximal operator due to which the evaluation of the Bellman function of this operator with respect to two variables is possible, as can be seen in [3]. Our inequality of interest is proved…

We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…

By a theorem of Greene and Wu, a noncompact connected Riemannian manifold admits a smooth strictly subharmonic exhaustion function. Demailly provided an elementary proof of this fact. A further simplification of Demailly's proof and some…

We analyze the differential relation corresponding to integrability of almost complex structures, reformulated as a directed immersion relation by Demailly and Gaussier. Combining results of Clemente [3], we show that applying h-principle…