32 citations · 90 across the 37 of their papers we have counts for
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Maximization of the second positive Neumann eigenvalue for planar domains
Alexandre Girouard, Nikolai Nadirashvili, Iosif Polterovich
We prove that the second positive Neumann eigenvalue of a bounded simply-connected planar domain of a given area does not exceed the first positive Neumann eigenvalue on a disk of…
On nodal sets and nodal domains on S^2 and R^2
Alexandre Eremenko, Dmitry Jakobson, Nikolai Nadirashvili
We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on S^2. We also construct a solution of the equa…
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…