4 citations · 4 across the 6 of their papers we have counts for
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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…
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…