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J. Korean Math. Soc. 1997; 34(4): 1037-1048

Printed December 1, 1997

Copyright © The Korean Mathematical Society.

Conformal compactification of ssymptotically Euclidean scalar-flat Kahler surfaces

Jongsu Kim

Sogang University

Abstract

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We show that an asymptotically Euclidean scalar-flat K\"{a}hler metric on a complex surface can be smoothly conformally compactified at the infinity point. We discuss some implication of this, characterizing such metrics on $\c^2$ blown up at some points.

Keywords: Conformal compactification, Scalar-flat K\"ahler surface, elliptic regularity

MSC numbers: Primary 53C21; Secondary 32L25

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