4 citations · 5 across the 3 of their papers we have counts for
6 papers · 1 filter
Morse inequalities for the area functional
Fernando C. Marques, Rafael Montezuma, André Neves
In this article we prove the strong Morse inequalities for the area functional in codimension one, assuming that the ambient dimension satisfies , in both th…
On free boundary minimal surfaces in the Riemannian Schwarzschild manifold
Rafael Montezuma
Is it possible to obtain unbounded minimal surfaces in certain asymptotically flat 3-manifolds as a limit of solutions to a natural mountain pass problem with diverging boundaries?…
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…
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…
Metrics of positive scalar curvature and unbounded widths
Rafael Montezuma
In this work we construct a sequence of Riemannian metrics on the three-sphere with scalar curvature greater than or equal to and arbitrarily large widths. Our procedure is bas…