Abstract
This paper examines the conjecture that $____udc$ is the global minimizer of the Dirichlet energy $I(____bu) = ____int_{B}|____nabla ____bu|^{2}____,d____bx$ among all $W^{1,2}$ mappings $____bu$ of the unit ball $B ____subset ____mathbb{R}^{2}$ satisfying (i) $____bu =____udc$ on $____partial B$, and (ii) $____det ____nabla ____bu = 1$ almost everywhere.