11 citations · 13 across the 4 of their papers we have counts for
5 papers · 1 filter
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…
Regularized traces and Taylor expansions for the heat semigroup
Michael Hitrik, Iosif Polterovich
We compute the coefficients in asymptotics of regularized traces and associated trace (spectral) distributions for Schrodinger operators, with short and long range potentials. A ke…