HCMU metrics with cusp singularities and conical singularities

An HCMU metric is a conformal metric which has a finite number of singularities on a compact Riemann surface and satisfies the equation of the extremal K"{a}hler metric. In this paper, we give a necessary and sufficient condition for the existence of a kind of HCMU metrics which has both cusp singularities and conical singularities.