Carleman Approximation of Maps into Oka Manifolds

24 Sep 2018 Chenoweth Brett

In this paper we obtain a Carleman approximation theorem for maps from Stein manifolds to Oka manifolds. More precisely, we show that under suitable complex analytic conditions on a totally real set $ M $ of a Stein manifold $X$, every smooth map $ X \rightarrow Y $ to an Oka manifold $Y$ satisfying the Cauchy-Riemann equations along $ M $ up to order $ k $ can be $ \mathscr{C}^k $-Carleman approximated by holomorphic maps $ X \rightarrow Y $... (read more)

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