Liouville Equation and Spherical Convex Polytopes
Feng Luo, Gang Tian · Proceedings of the American Mathematical Society · 1992
We study the Liouville equation $\Delta u = - {e^{2u}}$ in the complex plane with prescribed singularities and obtain a necessary and sufficient condition for the existence of the solution. The proof is based on the continuity method and a uniqueness theorem.