7 papers
Integral Formulas for Differential Forms on Weighted Manifolds and Applications
Fida El Chami, Ola Makhoul
In this paper, we derive a Reilly formula for differential forms on weighted manifolds with nonempty boundary. As an application of this formula, we prove a Poincaré-type inequalit…
The Buckling and Clamped Plate Problems on Differential Forms
Fida El Chami, Nicolas Ginoux, Georges Habib +2
We extend the buckling and clamped-plate problems to the context of differential forms on compact Riemannian manifolds with smooth boundary. We characterize their smallest eigenval…
New eigenvalue estimates involving Bessel functions
Fida El Chami, Nicolas Ginoux, Georges Habib
Given a compact Riemannian manifold (M n , g) with boundary M , we give an estimate for the quotient M f d g M f d g , where f is a smooth positive functi…
Rigidity results for Riemannian spin^c manifolds with foliated boundary
Fida Chami, Nicolas Ginoux, Georges Habib +1
Given a Riemannian spin^c manifold whose boundary is endowed with a Riemannian flow, we show that any solution of the basic Dirac equation satisfies an integral inequality dependin…
Eigenvalue Estimate for the basic Laplacian on manifolds with foliated boundary, part II
Fida El Chami, George Habib, Ola Makhoul +1
In [4], we gave a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic -forms defined on a compact manifold whose boundary is endowed with a Riemann…
Eigenvalue Estimate for the basic Laplacian on manifolds with foliated boundary
Fida El Chami, Georges Habib, Ola Makhoul +1
In this paper, we give a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic -forms defined on a compact manifold whose boundary is endowed with a…
Riemannian foliations with parallel or harmonic basic forms
Fida EL Chami, Georges Habib, Roger Nakad
In this paper, we consider a Riemannian foliation whose normal bundle carries a parallel or harmonic basic form. We estimate the norm of the O'Neill tensor in terms of the curvatur…