  It is shown that the estimates obtained by Manfredo P. do Carmo and Detang
Zhou, in their paper "Eigenvalue estimate on complete noncompact Riemannian
manifolds and applications", for the first eigenvalue of the Laplace-Beltrami
operator on open manifolds, via an oscillation theorem, can be naturally
extended for the semi-elliptic singular operator operator, p-Laplace on
manifolds.
