On Holomorphic Coverings of Planar Domains

We have previously shown that a $p$-fold holomorphic covering of a domain in the complex plane by another domain is extremal in the majorization principle for $p$-valent functions and quadratic forms associated with Green's functions of these domains. In this paper, dual majorization principles involving both Green's and Neumann functions are obtained, in which $p$-fold coverings are also extremal. The results are exemplified by applications of these principles to geometric function theory.