17 citations · 39 across the 18 of their papers we have counts for
18 papers
Index estimates for complete noncompact free boundary minimal surfaces
Marcos P. Cavalcante, Abraao Mendes, Ian R. dos Santos
Let be an unbounded domain with smooth boundary and let be a complete, noncompact, orientable, immersed free boundary minimal surface in , with compact…
Second Jacobi eigenvalues and spectral rigidity for surfaces in Berger spheres
Márcio Batista, Abraão Mendes
In this paper, we establish an upper bound for the second eigenvalue of the scalar Jacobi operator of an arbitrary closed two-sided surface immersed in a contracted Berger sphere.…
A strict second-eigenvalue estimate for the scalar stability operator on surfaces in
Márcio Batista, Abraão Mendes
Let be a closed immersed surface, with no orientability or, equivalently, two-sidedness assumptions. We establish the sharp quantitative estimat…
Second Eigenvalue Estimates and Spectral Rigidity for Submanifolds of Compact Rank-One Symmetric Spaces
Márcio Batista, Abraão Mendes
In this paper, we establish upper bounds for the second eigenvalue of the Schrödinger operator on -dimensional closed submanifolds of the compact projective spaces…
Index estimates for planar domains with Robin boundary condition
Abraão Mendes
In this note, we study the index of the Laplace operator on planar domains with compact smooth boundary, allowing both the compact and noncompact cases, under a natural Robin b…
Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator
Márcio Batista, Marcos P. Cavalcante, Abraão Mendes +1
In this paper, we investigate the spectral properties of the Jacobi operator for immersed surfaces with nonpositive Euler characteristic, extending previous results in the field. W…
Rigidity of min-max minimal disks in -balls with non-negative Ricci curvature
Laurent Mazet, Abraão Mendes
In this paper we prove a rigidity statement for free boundary minimal surfaces produced via min-max methods. More precisely, we prove that for any Riemannian metric on the 3-ba…
Some rigidity results for compact initial data sets
Gregory J. Galloway, Abraão Mendes
In this paper, we prove several rigidity results for compact initial data sets, in both the boundary and no boundary cases. In particular, under natural energy, boundary, and topol…
Free boundary minimal hypersurfaces outside of the ball
Laurent Mazet, Abraão Mendes
In this paper we obtain two classification theorems for free boundary minimal hypersurfaces outside of the unit ball (exterior FBMH for short) in Euclidean space. The first result…
Rigidity of free boundary MOTS
Abraão Mendes
The aim of this work is to present an initial data version of Hawking's theorem on the topology of back hole spacetimes in the context of manifolds with boundary. More precisely, w…
Initial data rigidity results
Michael Eichmair, Gregory J. Galloway, Abraão Mendes
We present several rigidity results for initial data sets motivated by the positive mass theorem. An important step in our proofs here is to establish conditions that ensure that a…
Vanishing theorems for the cohomology groups of free boundary hypersurfaces
Marcos P. Cavalcante, Abraão Mendes, Feliciano Vitório
In this paper, we prove that there exists a universal constant , depending only on positive integers and , such that if is a compact free boundary sub…
Characterization of hypersurfaces via the second eigenvalue of the Jacobi operator
Abraão Mendes
In this work we characterize certain immersed closed hypersurfaces of some ambient manifolds via the second eigenvalue of the Jacobi operator. First, we characterize the Clifford t…
Rigidity of volume-minimizing hypersurfaces in Riemannian 5-manifolds
Abraão Mendes
In this paper we generalize the main result of [4] for manifolds that are not necessarily Einstein. In fact, we obtain an upper bound for the volume of a locally volume-minimizing…
Rigidity of Marginally Outer Trapped (Hyper)Surfaces with Negative -Constant
Abraão Mendes
In this paper we generalize the main result of [13] in two different situations: in the first case for MOTSs of genus greater than one and, in the second case, for MOTSs of high di…
Rigidity of Free Boundary Surfaces in Compact 3-Manifolds with Strictly Convex Boundary
Abraão Mendes
In this paper we obtain an analogue of Toponogov theorem in dimension 3 for compact manifolds with nonnegative Ricci curvature and strictly convex boundary . Here…
Rigidity of marginally outer trapped 2-spheres
Gregory J. Galloway, Abraao Mendes
In a matter-filled spacetime, perhaps with positive cosmological constant, a stable marginally outer trapped 2-sphere must satisfy a certain area inequality. Namely, as discussed i…
Rigidity of marginally outer trapped 2-spheres
Abraão Mendes
In a recent work, Galloway [9] proved a local foliation theorem by MOTSs for a 3-dimensional initial data set with mean curvature in a 4-dimensional spacetime $(\…