Liouvilleʹs formula in arbitrary planar domains Original Research Article

This work extends to an arbitrary planar domain the global version of Liouvilleʹs formula for a general solution of the equation Δu=Ke-2u.Δu=Ke-2u. That equation is lifted to the universal covering space, where a solution is globally determined by a holomorphic function g,g, which is projected into a multivalued representation of the original solution. Applying the method to a punctured disk, results from Chou-Wan are unified and an integral formula for the solutions is derived.