5 citations · 10 across the 6 of their papers we have counts for
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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…
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…