A nonstiff boundary integral method for 3D free-surface flow with
surface tension is presented, with applications to porous media flow,
water waves, and hydroelastic waves. The velocity of the interface is
given in terms of the Birkhoff-Rott integral, and we present a new
method to compute this efficiently in doubly-periodic problems by
Ewald summation. The stiffness is removed by developing a small-scale
decomposition, in the spirit of prior work for 2D flow by Hou,
Lowengrub and Shelley. In order to develop this small scale
decomposition, we formulate this problem using a generalized
isothermal parameterization of the free surface.