18 citations · 90 across the 16 of their papers we have counts for
7 papers · 1 filter
One can't hear orientability of surfaces
Pierre Bérard, David L. Webb
The main result of this paper is that one cannot hear orientability of a surface with boundary. More precisely, we construct two isospectral flat surfaces with boundary with the sa…
Spectral positivity and Riemannian coverings
Pierre Bérard, Philippe Castillon
Let be a complete non-compact Riemannian manifold. We consider operators of the form , where is the non-negative Laplacian associated with the metric , an…
Inverse spectral positivity for surfaces
Pierre Bérard, Philippe Castillon
Let be a complete non-compact Riemannian surface. We consider operators of the form , where is the non-negative Laplacian, the Gaussian curvature, a…
Stability Properties of Rotational Catenoids in the Heisenberg Groups
Pierre Bérard, Marcos P. Cavalcante
In this paper, we determine the maximally stable, rotationally invariant domains on the catenoids $\cC_a$ (minimal surfaces invariant by rotations) in the Heisenberg group with a l…
Lindelöf's theorem for catenoids revisited
Pierre Bérard, Ricardo Sa Earp
In this paper we study the maximal stable domains on minimal catenoids in Euclidean and hyperbolic spaces and in . We in particular investigate whether half-vertical…
Examples of -hypersurfaces in and geometric applications
Pierre Bérard, Ricardo Sa Earp
In this paper we describe all rotation -hypersurfaces in and use them as barriers to prove existence and characterization of certain vertical -graphs and to gi…
Minimal hypersurfaces in $\HH^n \times \R$, total curvature and index
Pierre Bérard, Ricardo Sa Earp
In this paper, we consider minimal hypersurfaces in the product space . We begin by studying examples of rotation hypersurfaces and hypersurfaces in…