7 citations · 38 across the 29 of their papers we have counts for
18 papers · 1 filter
A Hilbert bundle approach to the sharp strong openness theorem and the Ohsawa-Takegoshi extension theorem
Tai Terje Huu Nguyen, Xu Wang
The following paper is around parts of the first named author's thesis. We discuss (what we call) a Hilbert bundle approach to complex Brunn-Minkowski theory and obtain a general m…
Gaussian Gabor frames, Seshadri constants and generalized Buser--Sarnak invariants
Franz Luef, Xu Wang
We investigate the frame set of regular multivariate Gaussian Gabor frames using methods from Kähler geometry such as Hörmander's $\dbar$- estimate with singular weight, Demai…
On a remark by Ohsawa related to the Berndtsson-Lempert method for -holomorphic extension
Tai Terje Huu Nguyen, Xu Wang
We utilize the Legendre-Fenchel transform and weak geodesics for plurisubharmonic functions to construct a weight function that can be used in the Berndtsson-Lempert method, to giv…
An explicit estimate of the Bergman kernel for positive line bundles
Xu Wang
We shall give an explicit estimate of the lower bound of the Bergman kernel associated to a positive line bundle. In the compact Riemann surface case, our result can be seen as an…
Bergman kernel and oscillation theory of plurisubharmonic functions
Bo-Yong Chen, Xu Wang
Based on Harnack's inequality and convex analysis we show that each plurisubharmonic function is locally BUO (bounded upper oscillation) with respect to polydiscs of finite type bu…
Notes on variation of Lefschetz star operator and -Hodge theory
Xu Wang
These notes were written to serve as an easy reference for \cite{Wang-AF}. All the results in this presentation are well-known (or quasi-well-known) theorems in Hodge theory. Our m…
A remark on the Alexandrov-Fenchel inequality
Xu Wang
In this article, we give a complex-geometric proof of the Alexandrov-Fenchel inequality without using toric compactifications. The idea is to use the Legendre transform and develop…
A flat Higgs bundle structure on the complexified Kähler cone
Xu Wang
We shall construct a natural Higgs bundle structure on the complexified Kähler cone of a compact Kähler manifold, which can be seen as an analogy of the classical Higgs bundle stru…
Relative $\dbar$-complex and its curvature properties
Xu Wang
We shall define the relative $\dbar$-complex and study the curvature properties of the associated vector bundles. As an application, we shall prove that Yamaguchi's theory on subha…
Curvature of higher direct image sheaves and its application on negative-curvature criterion for the Weil-Petersson metric
Xu Wang
We shall show that -semipositivity of the vector bundle over a Kähler total space implies the Griffiths-semipositivity of the -th direct image of $\mathcal O…
A curvature formula associated to a family of pseudoconvex domains
Xu Wang
We shall give a definition of the curvature operator for a family of weighted Bergman spaces associated to a smooth family of smoothly bounded strongly pseudocon…
Poincare Series And Very Ampleness Criterion For Pluri-canonical Bundles
Jujie Wu
Let be a compact quotient of a bounded domain in . Let be the canonical line bundle of . In this paper, we shall introduce the notion of very amplenes…
Ohsawa-Takegoshi type theorem and extension of plurisubharmonic functions
Bo-Yong Chen, Jujie Wu, Xu Wang
We prove a Thullen type extension theorem of plurisubharmonic functions across a closed complete pluripolar set, which generalizes a theorem of Siu. Our approach depends on an Ohsa…
Variation of Bergman kernels of pseudoconvex domains
Xu Wang
We shall give a variational formula of the full Bergman kernels associated to a family of smoothly bounded strongly pseudoconvex domains. An equivalent criterion for the triviality…
Variation of the Bergman kernels under deformations of complex structures
Xu Wang
Inspired by Berndtsson's work on the subharmonicity property of the Bergman kernel, we give a local variation formula of the full Bergman kernels associated to deformations of comp…
Covering stability of Bergman kernels on Kähler hyperbolic manifolds
Xu Wang
This paper is a sequel to \cite{Xu}. In this paper, an estimation of the Bergman Kernel of Kähler hyperbolic manifold is given by the estimate and the Bochner formula. As an…
Holomorphic maps with large images
Bo-Yong Chen, Xu Wang
We show that each pseudoconvex domain admits a holomorphic map to with , where is the minimum of…
Bergman completeness is not a quasi-conformal invariant
Xu Wang
We show that Bergman completeness is not a quasi-conformal invariant for general Riemann surfaces.