中文摘要：

HCMU度量是紧黎曼面上带奇点的extremal Khler度量.本文给出一个带锥奇点的非常曲率HCMU度量（non-CSC HCMU度量）的存在性定理,并讨论一般non-CSC HCMU度量的能量积分公式.

英文摘要：

An HCMU metric is an extremal Khler metric with singularities on a compact Riemann surface. We prove an existence theorem of non-CSC HCMU metrics with conical singularities,and discuss the energy integral formula for general non-CSC HCMU metrics.