4 citations · 5 across the 3 of their papers we have counts for
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math.DG2018
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…
math.DG2018
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…
math.DG2018
A mountain pass theorem for minimal hypersurfaces with fixed boundary
Rafael Montezuma
In this work, we prove the existence of a third embedded minimal hypersurface spanning a closed submanifold contained in the boundary of a compact Riemannian manifold with conv…