36 citations · 207 across the 27 of their papers we have counts for
28 papers
Dirac eigenvalues and spacetime mean curvature estimates for DEC spin fill-ins
Simon Raulot
We establish spacetime counterparts of fill-in inequalities for spin initial data sets satisfying the dominant energy condition in dimensions three through seven, controlling the m…
On the ADM mass of critical area-normalized capacitors
Simon Raulot
In this note, we prove mass-capacity inequalities for asymptotically flat manifolds whose boundary capacity potential satisfies an overdetermined problem, referred to as critical a…
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…
A Poincaré formula for differential forms and applications
Nicolas Ginoux, Georges Habib, Simon Raulot
We prove a new general Poincaré-type inequality for differential forms on compact Riemannian manifolds with nonempty boundary. When the boundary is isometrically immersed in Euclid…
Total mean curvature and first Dirac eigenvalue
Simon Raulot
In this note, we prove an optimal upper bound for the first Dirac eigenvalue of some hypersurfaces in Euclidean space by combining a positive mass theorem and the construction of q…
First boundary Dirac eigenvalue and boundary capacity potential
Simon Raulot
We derive new lower bounds for the first eigenvalue of the Dirac operator of an oriented hypersurface bounding a noncompact domain in a spin asymptotically flat manifold (M n ,…