New versions of Grötzsch principle and Reich-Strebel inequality

Abstract

In this note we will state a new version of Grötzsch's principle and using this principle we will sketch the proof of a generalization of the main inequality. Also, we will announce some related results and briefly explain that one can use new version of the main inequality to study uniqueness property of harmonic mapping in general. More details will be given in a forthcoming paper.