43 citations · 97 across the 8 of their papers we have counts for
6 papers · 1 filter
Remarks on J. Espinar's "Finite index operators on surfaces"
Pierre Bérard, Philippe Castillon
In this paper, we make some remarks on José Espinar's paper "Finite index operators on surfaces" [\texttt{arXiv:0911.3767}, to appear in Journal of Geometric Analysis (2011)].
On asymptotically harmonic manifolds of negative curvature
Philippe Castillon, Andrea Sambusetti
We study asymptotically harmonic manifolds of negative curvature, without any cocompactness or homogeneity assumption. We show that asymptotic harmonicity provides a lot of informa…
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…
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…
Submanifolds, Isoperimetric Inequalities and Optimal Transportation
Philippe Castillon
The aim of this paper is to prove isoperimetric inequalities on submanifolds of the Euclidean space using mass transportation methods. We obtain a sharp ?weighted isoperimetric ine…