# Linear invariants of complex manifolds and their plurisubharmonic variations

@inproceedings{Deng2019LinearIO,
title={Linear invariants of complex manifolds and their plurisubharmonic variations},
author={Fusheng Deng and Zhi-wei Wang and Liyou Zhang and Xiangyu Zhou},
year={2019}
}
• Fusheng Deng, +1 author Xiangyu Zhou
• Published 2019
• Mathematics
• For a bounded domain $D$ and a real number $p>0$, we denote by $A^p(D)$ the space of $L^p$ integrable holomorphic functions on $D$, equipped with the $L^p$- pseudonorm. We prove that two bounded hyperconvex domains $D_1\subset \mc^n$ and $D_2\subset \mc^m$ are biholomorphic (in particular $n=m$) if there is a linear isometry between $A^p(D_1)$ and $A^p(D_2)$ for some $0 2, p\neq 2,4,\cdots$, provided that the $p$-Bergman kernels on $D_1$ and $D_2$ are exhaustive. With this as a motivation, we… CONTINUE READING

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 34 REFERENCES

## A curvature formula associated to a family of pseudoconvex domains

• Xu Wang
• Mathematics
• 2015
VIEW 2 EXCERPTS
HIGHLY INFLUENTIAL

## Biholomorphic maps between Teichmüller spaces

VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

## Subharmonicity Properties of the Bergman Kernel and Some Other Functions Associated to Pseudoconvex Domains

VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

## New characterizations of plurisubharmonic functions and positivity of direct image sheaves.

• Mathematics
• 2018
VIEW 6 EXCERPTS

## An isometry theorem for quadratic differentials on Riemann surfaces of finite genus

VIEW 2 EXCERPTS
HIGHLY INFLUENTIAL

## An optimal $L^2$ extension theorem on weakly pseudoconvex Kähler manifolds

• Mathematics
• 2018
VIEW 2 EXCERPTS

## Ohsawa-Takegoshi Extension Theorem for Compact Kähler Manifolds and Applications

VIEW 3 EXCERPTS

## Algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Paun

• Mathematics
• 2016
VIEW 2 EXCERPTS

## Boundary behavior of the squeezing functions of complex domains

• Mathematics
• 2016
VIEW 1 EXCERPT

## Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces

• Mathematics
• 2016
VIEW 2 EXCERPTS