  The water wave problem is considered for a class of semi-infinite domains
each having its shore shaped as a cliffed cape. In particular, the free surface
of a water domain is supposed to be an infinite sector whose vertex angle is
greater than $\pi$, whereas the water layer lying under the free surface is of
constant depth. Under these assumptions, it is shown that there are no trapped
mode solutions of the problem for all values of a non-dimensional spectral
parameter; in other words, no point eigenvalues are embedded in the problem's
continuous spectrum.
