From the 2 of 5 linked papers with an AI index.
5 papers
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
The paper derives upper bounds for the second eigenvalue of a Schrödinger operator on closed submanifolds of compact rank‑one symmetric spaces and shows that equality forces the su…
First Eigenvalue of Jacobi operator and Rigidity Results for Constant Mean Curvature Hypersurfaces
Marcio Batista, Marcos P. Cavalcante, Luiz R. Melo
The paper derives geometric upper bounds for the first eigenvalue of the Jacobi operator on constant mean curvature hypersurfaces (both closed and with boundary) and uses these bou…
Serrin-type problem in divergence form on Riemannian manifolds
Márcio Batista, Márcio Santos, Antônio da Silva +1
In this paper, we investigate an overdetermined boundary value problem of divergence type on bounded domains in Riemannian manifolds with non-negative Ricci curvature. Using integr…
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…