arXiv subjects
Publications and source records attributed to Giang Le.
In this paper, we provide an integration by parts formula for plurisubharmonic functions on a hyperconvex domain that are bounded outside a compact set. This extends a previous result of Urban Cegrell.
In this paper, we study holomorphic curves satisfying the Fubini-Study derivative $\|f'(z)\|=O(|z|^σ)$ for some $σ>-1$ from the viewpoint of Nevanlinna theory
In this paper, we extend some recent results of Guedj-Lu-Zeriahi about psh envelopes of bounded functions on bounded domains in $\mathbb{C}^n$. We also present a result on the regularity of psh envelopes.
We establish an effective version of Schmidt's subspace theorem on a smooth projective variety $\mathcal{X}$ over function fields of characteristic zero for hypersurfaces located in m-subgeneral position with respect to $\mathcal{X}$. Our result generalizes and improves the results of An-Wang, Ru-Wang and the author.
In this paper, we study the Cauchy-Dirichlet problem for Parabolic complex Monge-Ampère equations on a strongly pseudoconvex domain by the viscosity method. We extend the results in [EGZ15b] on the existence of solution and the convergence at infinity. We also establish the Hölder regularity of the solutions when the Cauchy-Dirichlet data are Hölder continuous.
The action dimension of a discrete group $G$ is the minimum dimension of contractible manifold that admits a proper $G$-action. We compute the action dimension of the direct limit of a simple complex of groups for several classes of examples including: 1) Artin groups, 2) graph products of groups, and 3) fundamental groups of aspherical complements of arrangements of affine hyperplanes.
Our goal is to give Schmidt's subspace theorem for moving hypersurface targets in subgeneral position in projective varieties.
The \emph{action dimension} of a discrete group $G$ is the minimum dimension of a contractible manifold, which admits a proper $G$-action. In this paper, we study the action dimension of general Artin groups. The main result is that the action dimension of an Artin group with the nerve $L$ of dimension $n$ for $n \ne 2$ is less than or equal to $(2n + 1)$ if the Artin group satisfies the $K(π, 1)$-Conjecture and the top cohomology group of $L$ with $\mathbb{Z}$-coefficients is trivial. For $n = 2$, we need one more condition on $L$ to get the same inequality; that is the fundamental group of $L$ is generated by $r$ elements where $r$ is the rank of $H_1(L, \mathbb{Z})$.
We deduce an effective version of Schmidt's subspace theorem on a smooth projective variety X over function fields of characteristic zero for hypersurfaces located in N-subgeneral position with respect to X.
We study relatively hyperbolic Coxeter groups of type $HM$ with maximal Euclidean Coxeter subgroups of codimension 1. Our main result in this paper is that the dimension of these groups is bounded above.