Abstract
This paper is concerned with the low eigenvalues of closed surfaces in , of given measure, which are topologically equivalent to a sphere. Our aim is to obtain an isoprimetric inequality giving an upper bound for the product of the first three non-trivial eigenvalues of a convex closed surface topologically equivalent to a sphere. Moreover, we will also derive some lower bounds for the first non-trivial eigenvalue of the regular octahedron and icosahedron.
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