The extremal problem for weighted combined energy and $\ddot{I}-$Nitsche type inequality

Ting Peng, Chaochuan Wang, Xiaogao Feng

Let $A_1$ and $A_2$ be two circular annuli and let $\ddot{I}$ be a radial metric defined in the annuli $A_2$. We study the existence and uniqueness of the extremal problem for weighted c…