11 citations · 47 across the 15 of their papers we have counts for
18 papers
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…
Riemannian metrics on the sphere with Zoll families of minimal hypersurfaces
Lucas Ambrozio, Fernando C. Marques, André Neves
In this paper we construct smooth Riemannian metrics on the sphere which admit smooth Zoll families of minimal hypersurfaces. This generalizes a theorem of Guillemin for the case o…
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…
Bubbling analysis and geometric convergence results for free boundary minimal surfaces
Lucas Ambrozio, Reto Buzano, Alessandro Carlotto +1
We investigate the limit behaviour of sequences of free boundary minimal hypersurfaces with bounded index and volume, by presenting a detailed blow-up analysis near the points wher…
Geometric convergence results for closed minimal surfaces via bubbling analysis
Lucas Ambrozio, Reto Buzano, Alessandro Carlotto +1
We present some geometric applications, of global character, of the bubbling analysis developed by Buzano and Sharp for closed minimal surfaces, obtaining smooth multiplicity one c…
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…
A note on the index of closed minimal hypersurfaces of flat tori
Lucas Ambrozio, Alessandro Carlotto, Ben Sharp
Generalizing earlier work by Ros in ambient dimension three, we prove an affine lower bound for the Morse index of closed minimal hypersurfaces inside a flat torus in terms of thei…
A gap theorem for free boundary minimal surfaces in the three-ball
Lucas Ambrozio, Ivaldo Nunes
We show that, among free boundary minimal surfaces in the unit ball in the three-dimensional Euclidean space, the flat equatorial disk and the critical catenoid are characterised b…
Index estimates for free boundary minimal hypersurfaces
Lucas Ambrozio, Alessandro Carlotto, Ben Sharp
We show that the Morse index of a properly embedded free boundary minimal hypersurface in a strictly mean convex domain of the Euclidean space grows linearly with the dimension of…
Comparing the Morse index and the first Betti number of minimal hypersurfaces
Lucas Ambrozio, Alessandro Carlotto, Ben Sharp
By extending and generalising previous work by Ros and Savo, we describe a method to show that the Morse index of every closed minimal hypersurface on certain positively curved amb…
Compactness of the space of minimal hypersurfaces with bounded volume and p-th Jacobi eigenvalue
Lucas Ambrozio, Alessandro Carlotto, Ben Sharp
Given a closed Riemannian manifold of dimenion less than eight, we prove a compactness result for the space of closed, embedded minimal hypersurfaces satisfying a volume bound and…
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…
On perturbations of the Schwarzschild anti-de Sitter spaces of positive mass
Lucas C. Ambrozio
In this paper we prove the Penrose inequality for metrics that are small perturbations of the Schwarzschild anti-de Sitter metrics of positive mass. We use the existence of a globa…
Rigidity of area-minimizing free boundary surfaces in mean convex three-manifolds
Lucas C. Ambrozio
We prove a local splitting theorem for three-manifolds with mean convex boundary and scalar curvature bounded from below that contain certain locally area-minimizing free boundary…