Related papers: A note on characterizing pluriharmonic functions v…

In this article, we obtain an Ohsawa-Takegoshi-type $L^2$-extension for upper semi-continuous $L^2$-optimal functions via a Lebesgue-type differentiation theorem. As applications, we give a characterization of plurisubharmonic functions via…

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 Ohsawa-Takegoshi type extension theorem for a single point in a…

We give a new proof of Kiselman's minimum principle for plurisubharmonic functions, based on Ohsawa-Takegoshi extension theorem.

The celebrated Ohsawa--Takegoshi extension theorem for $L^2$ holomorphic functions on bounded pseudoconvex domains in $\mathbb C^n$ is a fundamental result in several complex variables and complex geometry. Ohsawa conjectured in 1995 that…

The key to the proof of the Ohsawa-Takegoshi Extension Theorem is a certain $\bar{\partial}$-estimate. The purpose of this note is to show that the 'curvature term' that arises in the Kohn-Morrey-H\"{o}rmander inequality (or the…

In this note, we show how to apply the original $L^2$-extension theorem of Ohsawa and Takegoshi to the standard basis of a multiplier ideal sheaf associated with a plurisubharmonic function. In this way, we are able to reprove the strong…

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 give an Ohsawa-Takegoshi extension type of result. Theorem 4.1…

This paper generalises the result of Jean-Pierre Demailly on his Ohsawa--Takegoshi-type $L^2$ extension theorem, which guarantees holomorphic extensions for some sections $f$ on analytic subspaces $Y$ defined by multiplier ideal sheaves of…

The purpose of this note is to show that the di-bar-estimate which is needed in the Ohsawa-Takegoshi Extension Theorem [6] is a direct consequence of the Hormander-Kohn-Morrey weigthed inequality. In this inequality, the Donnelly-Fefferman…

In this note, we answer a question on the extension of $L^{2}$ holomorphic functions posed by Ohsawa.

We present an $L^2$-extension theorem with an estimate depending on the weight functions for domains in $\mathbb{C}$. When the Hartogs domain defined by the weight function is strictly pseudoconvex, this estimate is strictly sharper than…

We prove a Liouville theorem for the plurisubharmonic functions on complete Kaelher manifolds. As the applications, we prove a splitting theorem for complete Kaehler manifolds with nonnegative biscetional curvature in terms of the linear…

In an influential $L^2$ extension theorem due to Demailly, the finiteness of an $L^2$ norm called the Ohsawa norm determines whether a given holomorphic function can be extended. This result has been further generalized by Zhou and Zhu to…

In this paper, we study global properties of continuous plurisubharmonic functions on complete noncompact K\"ahler manifolds with nonnegative bisectional curvature and their applications to the structure of such manifolds. We prove that…

Inspired by Chen-Wu-Wang (Math. Ann. 362: 305--319, 2015), we prove a Hartogs type extension theorem for plurisubharmonic functions across a compact complete pluripolar set, which is complementary to a classical theorem of Shiffman.

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

We study properties of relative types of plurisubharmonic functions with respect to maximal plurisubharmonic weights. It is shown that they give a general form for upper semicontinuous, tropically additive functionals on plurisubharmonic…

We give a simplified proof of an optimal version of the Ohsawa-Takegoshi $L^2$-extension theorem. We follow the variational proof by Berndtsson-Lempert and use the method in the paper of McNeal-Varolin. As an application, we give an optimal…

In this article we prove a theorem of Ohsawa-Takegoshi type on compact K\"ahler manifolds. Our arguments follow the "standard" approach for this kind of extension results; however, there are many complications arising from the…

The "qualitative" extension theorem of Demailly guarantees existence of holomorphic extensions of holomorphic sections on some subvariety under certain positive-curvature assumption, but that comes without any estimate of the extensions,…