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

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dc.creatorJakobson, D.
dc.creatorLevitin, M.
dc.creatorNadirashvili, N.
dc.creatorNigam, N.
dc.creatorPolterovich, I.
dc.date2005-09-18
dc.date.accessioned2026-07-07T06:18:09Z
dc.date.available2026-07-07T06:18:09Z
dc.descriptionSharp 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 that the first eigenvalue is maximized on a singular surface which is realized as a double branched covering over a sphere. The six ramification points are chosen in such a way that this surface has a complex structure of the Bolza surface. We prove that our conjecture follows from a lower bound on the first eigenvalue of a certain mixed Dirichlet-Neumann boundary value problem on a half-disk. The latter can be studied numerically, and we present conclusive evidence supporting the conjecture.
dc.description20 pages; 4 figures
dc.identifierhttps://arxiv.org/abs/math/0509398
dc.identifierhttp://arxiv.org/abs/math/0509398
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94641
dc.subjectSpectral Theory
dc.subjectMetric Geometry
dc.subject35P15; 47A75
dc.titleHow large can the first eigenvalue be on a surface of genus two?
dc.typetext

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