326 citations
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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.SP2003
Extremal metric for the first eigenvalue on a Klein bottle
Dmitry Jakobson, Nikolai Nadirashvili, Iosif Polterovich
The first eigenvalue of the Laplacian on a surface can be viewed as a functional on the space of Riemannian metrics of a given area. Critical points of this functional are called e…
math.SP2003
Arithmetic properties of eigenvalues of generalized Harper operators on graphs
J. Dodziuk, V. Mathai, S. Yates
Let $\Qbar$ denote the field of complex algebraic numbers. A discrete group is said to have the -multiplier algebraic eigenvalue property, if for every matrix with entri…