Removable Singularities of the cscK Metric

In this paper, we prove a removable singularity theorem for constant scalar curvature Kahler (cscK) metrics, which generalizes the result of Chen-He [3, Theorem 6.2]. Let f be a holomorphic function on Dn and denote S= {f = 0}. Suppose phi is an element of C-loc(infinity) (D-n\S) boolean AND L-infinity (Dn) boolean AND P SH(D-n\S) defines a cscK metric g phi = root-1 phi iover bar(j) dz(i) boolean AND dover bar(z)(j) on D-n\S. If there exist a constant C > 0 and a function theta(r)= o(1) as r -> 0 such that 1/C exp {-theta(|f|) | log | f||(1/2)} I <= g(phi) <= CI, where I = root-18(iover bar (j)) dz(i) boolean AND dover bar(z)(j), then g(phi) extends to a smooth cscK metric on D-n.