Approximation properties on spirallike domains of Cn

In this paper, we will show that any domain D in Cn which is spirallike with respect to a linear operator A, where m(A)>0, is Runge. We also show the local uniform approximation of biholomorphic mappings on a spirallike domain D with respect to A, where k+(A)<2m(A), by automorphisms of Cn. Finally, as an application of the above result, we will show that any Loewner PDE in a complete hyperbolic spirallike domain D with respect to A, where k+(A)<2m(A), of Cn admits an essentially unique univalent solution with values in Cn.