42 citations · 81 across the 16 of their papers we have counts for
23 papers
Rigidity and non-rigidity of the stable norm on
Fernando C. Marques, André Neves, Ao Sun
We show that the stable norm of flat metrics on is locally rigid if and locally rigid among metrics of the same volume if . We also sho…
Closed minimal surfaces of index one in Riemannian manifolds
Fernando C. Marques, André Neves
In this paper we prove that an -manifold, compactly -enlargeable, where , has connected, immersed Morse index one, closed minimal hypersurfaces with un…
Counting Minimal Lagrangians Via Mirzakhani Functions
Ben Lowe, Fernando C. Marques, André Neves
We show that for the number of genus minimal Lagrangians with area at most in a product of hyperbolic surfaces grows on the order of , with an explicit le…
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…
Conformal currents and the entropy of negatively curved three-manifolds
Fernando C. Marques, André Neves
In this paper, we describe the intersection between geodesic and conformal currents on closed hyperbolic three-manifolds. We use this to prove some sharp bounds which involve the L…
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…
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…
Counting minimal surfaces in negatively curved 3-manifolds
Danny Calegari, Fernando C. Marques, André Neves
We introduced an asymptotic quantity that counts area-minimizing surfaces in negatively curved closed 3-manifolds and show that quantity to only be minimized, among all metrics of…
Multiplicity one and strictly stable Allen-Cahn minimal hypersurfaces
Marco A. M. Guaraco, Fernando C. Marques, Andre Néves
We show that strictly stable components of Allen-Cahn minimal hypersurfaces always occur with multiplicity one. We also establish the uniqueness of solutions converging to nondegen…
Morse index of multiplicity one min-max minimal hypersurfaces
Fernando C. Marques, André Neves
In this paper, we prove that the Morse index of a multiplicity one, smooth, min-max minimal hypersurface is generically equal to the dimension of the homology class detected by the…
Equidistribution of minimal hypersurfaces for generic metrics
Fernando C. Marques, André Neves, Antoine Song
For almost all Riemannian metrics (in the Baire sense) on a closed manifold , , we prove that there is a sequence of closed, smooth, embedded…
Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature
Laurent Bessières, Gérard Besson, Sylvain Maillot +1
We prove that the moduli space of complete Riemannian metrics of bounded geometry and uniformly positive scalar curvature on an orientable 3-manifold is path-connected. This genera…
Density of minimal hypersurfaces for generic metrics
Kei Irie, Fernando C. Marques, André Neves
For almost all Riemannian metrics (in the Baire sense) on a closed manifold , , we prove that the union of all closed, smooth, embedded minim…
Weyl law for the volume spectrum
Yevgeny Liokumovich, Fernando C. Marques, André Neves
Given a Riemannian manifold with (possibly empty) boundary, we show that its volume spectrum satisfies a Weyl law that was conjectured by Gromov.
The catenoid estimate and its geometric applications
Daniel Ketover, Fernando C. Marques, André Neves
We prove a sharp area estimate for catenoids that allows us to rule out the phenomenon of multiplicity in min-max theory in several settings. We apply it to prove that i) the width…
Morse index and multiplicity of min-max minimal hypersurfaces
Fernando C. Marques, André Neves
The Min-max Theory for the area functional, started by Almgren in the early 1960s and greatly improved by Pitts in 1981, was left incomplete because it gave no Morse index estimate…
The Willmore conjecture
Fernando C. Marques, André Neves
The Willmore conjecture, proposed in 1965, concerns the quest to find the best torus of all. This problem has inspired a lot of mathematics over the years, helping bringing togethe…
Minimal surfaces - variational theory and applications
Fernando Coda Marques
Minimal surfaces are among the most natural objects in Differential Geometry, and have been studied for the past 250 years ever since the pioneering work of Lagrange. The subject i…
Existence of infinitely many minimal hypersurfaces in positive Ricci curvature
Fernando C. Marques, Andr'e Neves
In the early 1980s, S. T. Yau conjectured that any compact Riemannian three-manifold admits an infinite number of closed immersed minimal surfaces. We use min-max theory for the ar…
Min-max theory and the energy of links
Ian Agol, Fernando C. Marques, André Neves
Freedman, He, and Wang, conjectured in 1994 that the Mobius energy should be minimized, among the class of all nontrivial links in Euclidean space, by the stereographic projection…
Min-Max theory and the Willmore conjecture
Fernando C. Marques, André Neves
In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in Euclidean three-space is at least 2π^2. We prove this conjecture us…
Rigidity of min-max minimal spheres in three-manifolds
F. C. Marques, A. Neves
In this paper we consider min-max minimal surfaces in three-manifolds and prove some rigidity results. For instance, we prove that any metric on a 3-sphere which has scalar curvatu…
Deforming three-manifolds with positive scalar curvature
Fernando Coda Marques
In this paper we prove that the moduli space of metrics with positive scalar curvature of an orientable compact 3-manifold is path-connected. The proof uses the Ricci flow with sur…