Abstract
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(Ω), where Ω is the domain enclosed by M. More precise bounds are given when the ambient space is the complex or quaternionic hyperbolic space.
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Giménez, F., Miquel, V. & Orengo, J.J. Upper bounds of the first eigenvalue of closed hypersurfaces by the quotient area/volume. Arch. Math. 83, 279–288 (2004). https://doi.org/10.1007/s00013-004-4954-7
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DOI: https://doi.org/10.1007/s00013-004-4954-7