9 papers
Asymptotically conical shrinking ends of the -mean curvature flow: rotational construction and uniqueness
Hilário Alencar, Márcio Batista, Gregório Silva Neto
For we study shrinking self-similar ends of the -mean curvature flow, with , that are asymptotic to a cone. For every rotational…
An Abresch-Rosenberg type tensor and a gap theorem for CMC hypersurfaces in and
Hilário Alencar, Márcio Batista, Harold Rosenberg
We construct a symmetric trace-free tensor for constant-mean-curvature hypersurfaces in and that extends the Abresch-R…
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.…
Overdetermined equations and support functions on the hyperbolic and de Sitter planes
Márcio Batista, Iury Domingos
We study overdetermined equations on the hyperbolic and de Sitter planes by means of the support-function representation of zero mean curvature surfaces in Lorentz--Minkowski three…
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…
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…
First Eigenvalue of Jacobi operator and Rigidity Results for Constant Mean Curvature Hypersurfaces
Marcio Batista, Marcos P. Cavalcante, Luiz R. Melo
In this paper, we obtain geometric upper bounds for the first eigenvalue of the Jacobi operator for both closed hypersurfaces and compact hypersurfaces with boundary havin…