On first variation of Green's functions under quasiconformal deformation (Q914887)

The main results of this paper are general first variational formulas for Green's functions on arbitrary Riemann surfaces under quasiconformal deformation. In particular, Theorem 2 gives a formula which generalizes \textit{A. Sontag}'s one in [Arch. Rat. Mech. Analysis 59, 257-280 (1975; Zbl 0349.30014)] and \textit{F. Maitani}'s one in [J. Math. Kyoto Univ. 24, 49-66 (1984; Zbl 0433.30037)], while the formula in Theorem 3 generalizes another Sontag's and Guerrero's one in [\textit{I. Guerrero}, Mich. Math. J. 26, 351-360 (1979; Zbl 0433.30037)].