Parabolic metrics with conical singularities on compact Riemann surfaces

Abstract

In this paper, we prove the existence and uniqueness theorem for parabolic conical metrics on Riemann surfaces in the situation of generalized real angles, positive, zero and negative, by complex analysis, and give an example of this theorem to clarify concrete expressions of parabolic metrics on the two-sphere and generalize the well-known Schwarz-Christoffel formula.