  In 1960, Payne and Weinberger proved that among all domains that lie within a
wedge (an angle whose measure is less than or equal to $\pi$), and have a given
value of a certain integral the circular sector has the lowest fundamental
eigenvalue of the Dirichlet Laplacian. Here, it is shown that an analogue of
this assertion is true for domains with a cut and for indented domains; that
is, for those located in a reflex angle (its measure is between $\pi$ and $2
\pi$).
