26 citations · 28 across the 6 of their papers we have counts for
6 papers
Courant-sharp eigenvalues of compact flat surfaces: Klein bottles and cylinders
Pierre Bérard, Bernard Helffer, Rola Kiwan
The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp…
Non-boundedness of the number of super level domains of eigenfunctions
Pierre Bérard, Philippe Charron, Bernard Helffer
Generalizing Courant's nodal domain theorem, the "Extended Courant property" is the statement that a linear combination of the first eigenfunctions has at most nodal domain…
Some nodal properties of the quantum harmonic oscillator and other Schr{ö}dinger operators in
Pierre Bérard, Bernard Helffer
For the spherical Laplacian on the sphere and for the Dirichlet Laplacian in the square}, Antonie Stern claimed in her PhD thesis (1924) the existence of an infinite sequence of ei…
Courant-sharp eigenvalues for the equilateral torus, and for the equilateral triangle
Pierre Bérard, Bernard Helffer
We address the question of determining the eigenvalues (listed in nondecreasing order, with multiplicities) for which Courant's nodal domain theorem is sharp i.e., for which…
Eigenvalue estimates for hypersurfaces in and applications
Pierre Bérard, Philippe Castillon, Marcos P. Cavalcante
In this paper, we give a lower bound for the spectrum of the Laplacian on minimal hypersurfaces immersed into . As an application, in dimension 2, we prove that a com…
Index Growth of hypersurfaces with constant mean curvature
Pierre Bérard, Levi Lopes de Lima, Wayne Rossman
In this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature (cmc) 1 in (Delaunay unduloids). When , using…