Classical and modern majorization principles for meromorphic functions on domains of the Riemann sphere are considered. We first discuss Lindel枚f's principle on the behavior of Green's functions under a holomorphic mapping. Then generalizations of this principle are given with the replacement of Green's functions by Robin's functions. Next, we consider IP Mityuk's dual dominance principle and some of its applications to polynomials and rational functions. Finally, new dual principles of dominance on the behavior under holomorphic mappings of quadratic forms, including Green's functions and Neumann's functions, are presented. Some applications of these principles and the symmetrization of condensers in the geometric theory of functions are given.
