11 citations · 11 across the 1 of their papers we have counts for
4 papers
On the min-max width of unit volume three-spheres
Lucas Ambrozio, Rafael Montezuma
How large can be the width of Riemannian three-spheres of the same volume in the same conformal class? If a maximum value is attained, how does a maximising metric look like? What…
On the two-systole of real projective spaces
Lucas Ambrozio, Rafael Montezuma
We establish an integral-geometric formula for minimal two-spheres inside homogeneous three-spheres, and use it to provide a characterisation of each homogeneous metric on the thre…
Compactness analysis for free boundary minimal hypersurfaces
Lucas Ambrozio, Alessandro Carlotto, Ben Sharp
We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions tha…
On static three-manifolds with positive scalar curvature
L. Ambrozio
We compute a Bochner type formula for static three-manifolds and deduce some applications in the case of positive scalar curvature. We also explain in details the known general con…