Zobrazeno 1 - 10
of 119
pro vyhledávání: '"Lu, Chinh H."'
We study the volumes of transcendental and possibly non-closed Bott-Chern $(1,1)$-classes on an arbitrary compact complex manifold $X$. We show that the latter belongs to the class $\mathcal{C}$ of Fujiki if and only if it has the $\textit{bounded ma
Externí odkaz:
http://arxiv.org/abs/2406.01090
We initiate the study of $m$-subharmonic functions with respect to a semipositive $(1,1)$-form in Euclidean domains, providing a significant element in understanding geodesics within the context of complex Hessian equations. Based on the foundational
Externí odkaz:
http://arxiv.org/abs/2405.04948
This study examines geodesics and plurisubharmonic envelopes within the Cegrell classes on bounded hyperconvex domains in $\mathbb{C}^n$. We establish that solutions possessing comparable singularities to the complex Monge-Amp\`ere equation are ident
Externí odkaz:
http://arxiv.org/abs/2405.04384
Given a compact K\"ahler manifold, we survey the study of complex Monge-Amp\`ere type equations with prescribed singularity type, developed by the authors in a series of papers. In addition, we give a general answer to a question of Guedj--Zeriahi ab
Externí odkaz:
http://arxiv.org/abs/2303.11584
Autor:
Guedj, Vincent, Lu, Chinh H.
In this note we provide uniform a priori estimates for solutions to degenerate complex Hessian equations on compact hermitian manifolds. Our approach relies on the corresponding a priori estimates for Monge-Amp\`ere equations; it provides an extensio
Externí odkaz:
http://arxiv.org/abs/2302.03354
Let $(X,\omega)$ be a compact hermitian manifold of dimension $n$. We study the asymptotic behavior of Monge-Amp\`ere volumes $\int_X (\omega+dd^c \varphi)^n$, when $\omega+dd^c \varphi$ varies in the set of hermitian forms that are $dd^c$-cohomologo
Externí odkaz:
http://arxiv.org/abs/2207.04705
Autor:
Di Nezza, Eleonora, Lu, Chinh H.
We prove a geodesic distance formula for quasi-psh functions with finite entropy, extending results by Chen and Darvas. We work with big and nef cohomology classes: a key result we establish is the convexity of the $K$-energy in this general setting.
Externí odkaz:
http://arxiv.org/abs/2112.09627
Autor:
Guedj, Vincent, Lu, Chinh H.
We develop a new approach to $L^{\infty}$-a priori estimates for degenerate complex Monge-Amp\`ere equations on complex manifolds. It only relies on compactness and envelopes properties of quasi-plurisubharmonic functions. In a prequel \cite{GL21a} w
Externí odkaz:
http://arxiv.org/abs/2107.01938
Autor:
Guedj, Vincent, Lu, Chinh H.
We develop a new approach to $L^{\infty}$-a priori estimates for degenerate complex Monge-Amp\`ere equations on complex manifolds. It only relies on compactness and envelopes properties of quasi-plurisubharmonic functions. Our method allows one to ob
Externí odkaz:
http://arxiv.org/abs/2106.04273
Autor:
Guedj, Vincent, Lu, Chinh H.
Publikováno v:
Algebraic Geometry 9 (6) (2022) 688--713
In \cite{GL21a} we have developed a new approach to $L^{\infty}$-a priori estimates for degenerate complex Monge-Amp\`ere equations, when the reference form is closed. This simplifying assumption was used to ensure the constancy of the volumes of Mon
Externí odkaz:
http://arxiv.org/abs/2106.04272