Analytic continuation in mapping spaces

Abstract

We consider a Stein manifold $M$ of dimension $\ge 2$ and a compact subset $K\subset M$ such that $M^{\prime }=M\backslash K$ is connected. Let $S$ be a compact differential manifold, and let $M_S$, resp. $M_S^{\prime }$ stand for the complex manifold of maps $S\to M$, resp. $S\to M^{\prime }$, of some specified regularity, that are homotopic to constant. We prove that any holomorphic function on $M_S^{\prime }$ continues analytically to $M_S$ (perhaps as a multivalued function).

24 pages

References in corpus (1)

• Analytic cohomology in a Banach space