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oydeis
oydeis
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Suppose $M$ is a complex manifold and $\Omega$ a (edit: bounded) pseudoconvex domain in $M$. Let $u:M\setminus\Omega\to\mathbb{R}$ be a pluriharmonic function. Is it true that $u$ has a pluriharmonic extension to $M$? edit: $dim_{\mathbb{C}}(M)>2$$dim_{\mathbb{C}}(M)\geq 2$.

Suppose $M$ is a complex manifold and $\Omega$ a pseudoconvex domain in $M$. Let $u:M\setminus\Omega\to\mathbb{R}$ be a pluriharmonic function. Is it true that $u$ has a pluriharmonic extension to $M$? edit: $dim_{\mathbb{C}}(M)>2$.

Suppose $M$ is a complex manifold and $\Omega$ a (edit: bounded) pseudoconvex domain in $M$. Let $u:M\setminus\Omega\to\mathbb{R}$ be a pluriharmonic function. Is it true that $u$ has a pluriharmonic extension to $M$? edit: $dim_{\mathbb{C}}(M)\geq 2$.

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oydeis
oydeis
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Suppose $M$ is a complex manifold and $\Omega$ a pseudoconvex domain in $M$. Let $u:M\setminus\Omega\to\mathbb{R}$ be a pluriharmonic function. Is it true that $u$ has a pluriharmonic extension to $M$? edit: $dim_{\mathbb{C}}(M)>2$.

Suppose $M$ is a complex manifold and $\Omega$ a pseudoconvex domain in $M$. Let $u:M\setminus\Omega\to\mathbb{R}$ be a pluriharmonic function. Is it true that $u$ has a pluriharmonic extension to $M$?

Suppose $M$ is a complex manifold and $\Omega$ a pseudoconvex domain in $M$. Let $u:M\setminus\Omega\to\mathbb{R}$ be a pluriharmonic function. Is it true that $u$ has a pluriharmonic extension to $M$? edit: $dim_{\mathbb{C}}(M)>2$.

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oydeis
oydeis
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  • 3

Extension of pluriharmonic functions

Suppose $M$ is a complex manifold and $\Omega$ a pseudoconvex domain in $M$. Let $u:M\setminus\Omega\to\mathbb{R}$ be a pluriharmonic function. Is it true that $u$ has a pluriharmonic extension to $M$?