Ismail Kombe SHARP WEIGHTED RELLICH AND UNCERTAINTY PRINCIPLE INEQUALITIES ON CARNOT GROUPS (312K, PDF) ABSTRACT. In this work we prove sharp weighted Rellich-type inequalities and their improved versions for general Carnot groups. To derive the improved Rellich-type inequalities we have established new weighted Hardy-type inequalities with remainder terms. We also prove new sharp forms of the weighted Hardy-Poincare and uncertainty principle inequalities for polarizable Carnot groups.