7 papers · 1 filter
Topology of stable free boundary CMC surfaces under lower Ricci curvature bounds
Railane Antonia, Marcos P. Cavalcante, Vinicius Souza
We establish intrinsic area--length--topology inequalities for compact free boundary constant mean curvature (CMC) surfaces in three-manifolds with Ricci curvature bounded from bel…
Second Robin eigenvalue bounds for Schrödinger operators on Riemannian surfaces
Railane Antonia, Marcos P. Cavalcante, Vinicius Souza
Let be a compact Riemannian surface, possibly with boundary, and consider Schrödinger-type operators of the form together with natural Robin and Steklov-typ…
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…
Stability of extremal domains for the first eigenvalue of the Laplacian operator
Marcos P. Cavalcante, Ivaldo Nunes
In this paper, we compute the second variation of the first Dirichlet eigenvalue on extremal domains in general Riemannian manifolds and establish a criterion for stability. We cla…
Index estimates for harmonic Gauss maps
Alcides de Carvalho, Marcos P. Cavalcante, Wagner Costa-Filho +1
Let denote a closed surface with constant mean curvature in , a 3-dimensional Lie group equipped with a bi-invariant metric. For such surfaces, there is a harmoni…
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…