11 citations · 15 across the 5 of their papers we have counts for
7 papers
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…
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…
Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond
Dmitry Jakobson, Michael Levitin, Nikolai Nadirashvili +1
Consider a bounded domain with the Dirichlet condition on a part of the boundary and the Neumann condition on its complement. Does the spectrum of the Laplacian determine uniquely…
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…
Eigenvalue spacings for regular graphs
D. Jakobson, S. D. Miller, I. Rivin +1
We carry out a numerical study of fluctuations in the spectrum of regular graphs. Our experiments indicate that the level spacing distribution of a generic k-regular graph approach…
Extremal metrics on graphs I
Dmitry Jakobson, Igor Rivin
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces…