From the 1 of 4 linked papers with an AI index.
4 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…
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…
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…