Smooth Extensions and Spaces of Smooth and Holomorphic Mappings

Abstract

In this paper we present a new notion of a smooth manifold with corners and relate it to the commonly used concept in the literature. We also introduce complex manifolds with corners show that if $M$ is a compact (respectively, complex) manifold with corners and $K$ is a smooth (respecti vely, complex) Lie group, then $C^{\infty}(M, K)$ (respectively, $\mathcal{O}(M, K)$) is a smooth (respectively, complex) Lie group.