# 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} }

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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