Upper bounds of the first eigenvalue of closed hypersurfaces by the quotient area/volume
In this paper we obtain, for compact hypersurfaces M embedded into Hadamard
manifolds, an upper sharp bound of the first closed eigenvalue. This bound depends on the isoperimetric
quotient Volume(M)/Volume(U), where U is the domain enclosed by M. More precise
bounds are given when the ambient space is the complex or quaternionic hyperbolic space.