Boundary variation and quasiconformal maps of Riemann surfaces (Q2367106)

In Kodai Math. J. 12, No. 3, 283-295 (1989; Zbl 0697.30045) the author has developed a method to obtain second variational formulas for fundamental quantities on Riemann surfaces under quasiconformal deformations. In this paper it is shown that these formulas imply some general ones under boundary variation. In particular the classical Garabedian-Schiffer formula under Hadamard variation and some of Yamaguchi's formulas are contained as special cases. In this paper only values of Green's functions are studied. It is claimed that other cases can be discussed using the same arguments.