11 citations · 12 across the 4 of their papers we have counts for
8 papers · 1 filter
Ambient geometry via min-max widths of embedded circles
Lucas Ambrozio, Ivan Miranda, Rafael Montezuma
We prove a lower bound for the Birkhoff min-max invariant of a Riemannian sphere in terms of the min-max width of its embedded circles. The main tool is a method to induce a sweepo…
Rigidity theorems for the area widths of Riemannian manifolds
Lucas Ambrozio, Fernando C. Marques, André Neves
The volume spectrum of a compact Riemannian manifold is a sequence of critical values for the area functional, defined in analogy with the Laplace spectrum by Gromov. In this paper…
The intrinsic metric of constant mean curvature surfaces and minimal hypersurfaces with free boundary
Lucas Ambrozio
Ricci-Curbastro established necessary and sufficient conditions for a Riemannian metric on a surface to be the first fundamental form of a minimal immersion of that surface into th…
The width of embedded circles
Lucas Ambrozio, Rafael Montezuma, Roney Santos
We develop a Morse-Lusternik-Schnirelmann theory for the distance between two points of a smoothly embedded circle in a complete Riemannian manifold. This theory suggests very natu…
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…