Lower bounds of Cheeger-Osserman type for the first eigenvalue of then-dimensional fixed membrane problem

Summary In this note we derive new lower bounds for the first eigenvalue of the Laplacian in a boundedn-dimensional domain with Dirichlet boundary conditions. The lower bounds obtained are related to those of Cheeger (1970) 2] and Osserman (1977) 6], and they turn out to be sharper when the domain is not too far from being a ball.This work has been supported by the DGICYT project PB86-0306. It was done while the second author was visiting the Department of Mathematics of Heriot-Watt University, with the support of a Fleming Award 1988/89.