### Analytic continuation in mapping spacesAnalytic continuation in mapping spaces

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 Author Lempert, Laszlo Source arXiv.org Content type Text File Format PDF Date of Submission 2008-08-12 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Complex Variables ♦ 58B12 ♦ 46G20 ♦ 32D ♦ 58D15 ♦ math Abstract We consider a Stein manifold $M$ of dimension $\geq 2$ and a compact subset $K\subset M$ such that $M'=M\backslash K$ is connected. Let $S$ be a compact differential manifold, and let $M_S$, resp. $M'_S$ stand for the complex manifold of maps $S\to M$, resp. $S\to M'$, of some specified regularity, that are homotopic to constant. We prove that any holomorphic function on $M'_S$ continues analytically to $M_S$ (perhaps as a multivalued function). Educational Use Research Learning Resource Type Article Page Count 24