5 citations · 11 across the 32 of their papers we have counts for
33 papers
An algebraic approach to the existence of valuative interpolation
Shijie Bao, Qi'an Guan, Zhitong Mi +1
An algebraic approach is presented for the valuative interpolation problem, which recovers and generalizes prior characterizations known in the complex analytic setting by the auth…
The existence of valuative interpolation at a singular point
Shijie Bao, Qi'an Guan, Zhitong Mi +1
The present paper studies the existence of valuative interpolation on the local ring of an irreducible analytic subvariety at singular points. We firstly develop the concepts and m…
The existence of valuative interpolation
Shijie Bao, Qi'an Guan, Zhitong Mi +1
In this article, using key tools including Zhou valuations, Tian functions and a convergence result for relative types, we establish necessary and sufficient conditions for the exi…
A remark on a generalized Suita conjecture for finite points case
Qi'an Guan, Xun Sun, Zheng Yuan
In this article, we use a class of harmonic functions (maybe multi-valued) to study the equality part in a weighted version of Suita conjecture for higher derivatives and finite po…
Weighted versions of Saitoh's conjecture in fibration cases
Qi'an Guan, Gan Li, Zheng Yuan
In this article, we introduce some generalized Hardy spaces on fibrations of planar domains and fibrations of products of planar domains. We consider the kernel functions on these…
On the multipoled global Zhou weights and semi-continuity for Zhou numbers
Shijie Bao, Qi'an Guan, Zhitong Mi +1
In the present paper, we give the definition and properties of the multipoled global Zhou weights. Some approximation and convergence results of multipoled global Zhou weights are…
Zhou valuations and jumping numbers
Shijie Bao, Qi'an Guan, Zheng Yuan
In this article, we prove that for any Zhou valuation , there exists a graded sequence of ideals and a nonzero ideal such that $\math…
Tame maximal weights, relative types and valuations
Shijie Bao, Qi'an Guan, Zhitong Mi +1
In this article, we obtain a class of tame maximal weights (Zhou weights). Using Tian functions (the function of jumping numbers with respect to the exponents of a holomorphic func…
A generalization of the conjugate Hardy spaces
Qi'an Guan, Zheng Yuan
In this article, we consider a generalization of the conjugate Hardy spaces, and give some properties of the minimal norm of the generalization and some relations between the…
Concavity property of minimal integrals with Lebesgue measurable gain VIII -- partial linearity and log-convexity
Shijie Bao, Qi'an Guan, Zheng Yuan
In this article, we give some necessary conditions for the concavity property of minimal integrals degenerating to partial linearity, a charaterization for the concavity dege…
Minimal integrals for the Hardy spaces and the Bergman spaces
Qi'an Guan, Zheng Yuan
In this article, we consider the minimal integrals for the Hardy spaces and the Bergman spaces, and we present some relations between them, which can be regarded as the solut…
The log-plurisubharmonicity of fiberwise Bergman kernels for variant functionals
Shijie Bao, Qi'an Guan, Zheng Yuan
In this paper, we establish the log-plurisubharmonicity of fiberwise -Bergman kernels for a family of variant functionals, thereby addressing a question posed by Bo Berndtsson t…
A remark on a weighted version of Suita conjecture for higher derivatives
Qi'an Guan, Xun Sun, Zheng Yuan
In this article, we consider the set of points for the holding of the equality in a weighted version of Suita conjecture for higher derivatives, and give relations between the set…
A note on Bergman kernels
Shijie Bao, Qi'an Guan, Zheng Yuan
In the present note, we introduce the complex singularity exponents, which come from the asymptotic property of Bergman kernels on sub-level sets of plurisubharmonic functi…
Concavity property of minimal integrals with Lebesgue measurable gain VI: fibrations over products of open Riemann surfaces
Shijie Bao, Qi'an Guan, Zheng Yuan
In this article, we present characterizations of the concavity property of minimal integrals degenerating to linearity in the case of fibrations over products of open Riemann…
Concavity property of minimal integrals with Lebesgue measurable gain IV: product of open Riemann surfaces
Qi'an Guan, Zheng Yuan
In this article, we present characterizations of the concavity property of minimal integrals degenerating to linearity in the case of products of analytic subsets on products…
A Remark on Optimal extension theorem for holomorphic vector bundles
Qi'an Guan, Zhitong Mi, Zheng Yuan
In this note, we present an optimal extension theorem for holomorphic vector bundles with smooth hermitian metrics for continuous gain on weakly pseudoconvex Kähler manifolds…
Concavity property of minimal integrals with Lebesgue measurable gain III: open Riemann surfaces
Qi'an Guan, Zheng Yuan
In this article, we present a characterization of the concavity property of minimal integrals degenerating to linearity in the case of finite points on open Riemann surfaces.…
Concavity property of minimal integrals with Lebesgue measurable gain II
Qi'an Guan, Zhitong Mi, Zheng Yuan
In this article, we present a concavity property of the minimal integrals related to multiplier ideal sheaves with Lebesgue measurable gain on weakly pseudoconvex Kähler ma…
Concavity property of minimal integrals with Lebesgue measurable gain V--fibrations over open Riemann surfaces
Shijie Bao, Qi'an Guan, Zheng Yuan
In this article, we present characterizations of the concavity property of minimal integrals degenerating to linearity in the case of fibrations over open Riemann surfaces. A…
Hardy space, kernel function and Saitoh's conjecture on products of planar domains
Qi'an Guan, Zheng Yuan
In this article, we consider two classes of weighted Hardy spaces on products of planar domains and their corresponding kernel functions, and we prove product versions of Saitoh's…
Optimal extension for holomorphic vector bundles with singular hermitian metrics
Qi'an Guan, Zhitong Mi, Zheng Yuan
In the present paper, we study the properties of singular Nakano positivity of singular hermitian metrics on holomorphic vector bundles, and establish an optimal extension th…
Concavity property of minimal integrals with Lebesgue measurable gain
Qi'an Guan, Zheng Yuan
In this article, we present a concavity property of the minimal integrals related to multiplier ideal sheaves with Lebesgue measurable gain. As applications, we give necessar…
A weighted version of Saitoh's conjecture
Qi'an Guan, Zheng Yuan
In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.