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The moduli space of extremal compact Kähler manifolds and generalized Weil-Petersson metrics

1990
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Publications of the Research Institute for Mathematical Sciences
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where j is the natural inclusion. Proposition 1.1. Let S Teg be the set of smooth points of S. Let (p e F(S, ^S(R)) be a C°° function whose restriction to S reg is pluriharmonic. Then (p is pluriharmonic on the whole S. Proof. We extend the argument in the proof of [Fu2; Lemma 6]. Since the problem is local, we fix a point o e S and prove that we can ^n^ a holomorphic function / on S with Im / = <p, determined up to additive real constants on each connected component of S. By adjusting these

doi:10.2977/prims/1195171664
fatcat:twfnelnwfjccbl4acis2l744tq