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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.SP2005
Estimates from below for the spectral function and for the remainder in local Weyl's law
Dmitry Jakobson, Iosif Polterovich
We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on manifolds. In the negatively curved case, thermodynamic fo…