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MR1724211 (2001c:53045) 53C21 (53C12 53C20)
Smyth, Brian; Xavier, Frederico Real solvability of the equation $\partial\sp 2\sb {\overline z}\omega=\rho g$ and the topology of isolated umbilics. J. Geom. Anal. 8 (1998), no. 4, 655–671.
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