  The notion of non-degenerate solutions for the dispersionless Toda hierarchy
is generalized to the universal Whitham hierarchy of genus zero with $M+1$
marked points. These solutions are characterized by a Riemann-Hilbert problem
(generalized string equations) with respect to two-dimensional canonical
transformations, and may be thought of as a kind of general solutions of the
hierarchy. The Riemann-Hilbert problem contains $M$ arbitrary functions
$H_a(z_0,z_a)$, $a = 1,...,M$, which play the role of generating functions of
two-dimensional canonical transformations. The solution of the Riemann-Hilbert
problem is described by period maps on the space of $(M+1)$-tuples
$(z_\alpha(p) : \alpha = 0,1,...,M)$ of conformal maps from $M$ disks of the
Riemann sphere and their complements to the Riemann sphere. The period maps are
defined by an infinite number of contour integrals that generalize the notion
of harmonic moments. The $F$-function (free energy) of these solutions is also
shown to have a contour integral representation.
