Our goal is a method for getting lower bounds for
the lowest eigenvalue
of a manifold M.
Among several equivalent definitions for ,
the following will be most convenient to work with:
Definition.
Let M be a non-compact complete
n-dimensional Riemannian manifold with boundary.
Let TF(M)
(``test functions'')
denote the set of 
functions 
that have compact support and do not vanish identically.
We define 
as the infimum over TF(M)
of the Rayleigh quotient
