REILLY INEQUALITIES OF ELLIPTIC OPERATORS ON CLOSED SUBMANIFOLDS

Using generalized position vector fields we obtain new upper bound estimates of the first nonzero eigenvalue of a kind of elliptic operator on closed submanifolds isometrically immersed in Riemannian manifolds of bounded sectional curvature. Applying these Reilly inequalities we improve a series of recent upper bound estimates of the first nonzero eigenvalue of the L-r operator on closed hypersurfaces in space forms.