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KConrad
KConrad
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Suppose $M$ and $N$ are two Stein manifolds of dimension at least $3$ with compact subsets $U$ and $V$ such that $M\setminus U$ is byholomorphicbiholomorphic to $N \setminus V$. It it turetrue that $M$ is byholomorphicbiholomorphic to $N$?

It this is not true, what is the simplest example? And if this is turetrue, what would be the refferencereference for such a statement?

Suppose $M$ and $N$ are two Stein manifolds of dimension at least $3$ with compact subsets $U$ and $V$ such that $M\setminus U$ is byholomorphic to $N \setminus V$. It it ture that $M$ is byholomorphic to $N$?

It this is not true, what is the simplest example? And if this is ture, what would be the refference for such a statement?

Suppose $M$ and $N$ are two Stein manifolds of dimension at least $3$ with compact subsets $U$ and $V$ such that $M\setminus U$ is biholomorphic to $N \setminus V$. It it true that $M$ is biholomorphic to $N$?

It this is not true, what is the simplest example? And if this is true, what would be the reference for such a statement?

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Dmitri Panov
Dmitri Panov
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Stein manifolds isomorphic at infinity

Suppose $M$ and $N$ are two Stein manifolds of dimension at least $3$ with compact subsets $U$ and $V$ such that $M\setminus U$ is byholomorphic to $N \setminus V$. It it ture that $M$ is byholomorphic to $N$?

It this is not true, what is the simplest example? And if this is ture, what would be the refference for such a statement?