most citedHow large can the first eigenvalue be on a surface of genus two?

11 citations · 11 across the 1 of their papers we have counts for

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2 papers

math.SP2005★ 11 cited

How large can the first eigenvalue be on a surface of genus two?

D. Jakobson, M. Levitin, N. Nadirashvili +2

Sharp upper bounds for the first eigenvalue of the Laplacian on a surface of a fixed area are known only in genera zero and one. We investigate the genus two case and conjecture th…

math.AP1998

Bounds on the multiplicity of eigenvalues for fixed membranes

Thomas Hoffman-Ostenhof, Peter W. Michor, Nikolai Nadirashvili

For a membrane in the plane the multiplicity of the -th eigenvalue is known to be not greater than . Here we prove that it is actually not greater than , for $k\ge 3…