25 citations · 25 across the 10 of their papers we have counts for
12 papers
Index estimates for complete noncompact free boundary minimal surfaces
Marcos P. Cavalcante, Abraao Mendes, Ian R. dos Santos
Let be an unbounded domain with smooth boundary and let be a complete, noncompact, orientable, immersed free boundary minimal surface in , with compact…
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…
On the Dirichlet boundary value problem on Cartan-Hadamard manifolds
Marcos P. Cavalcante, José M. Espinar, Diego A. Marín
We study bounded solutions of Dirichlet boundary value problems for semilinear elliptic equations on Cartan-Hadamard manifolds with pinched negative curvature. We prove nonexistenc…
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…
Geometric properties of extremal domains for the -Laplacian operator
Francisco G. Carvalho, Marcos P. Cavalcante
In this paper, we explore the geometric properties of unbounded extremal domains for the -Laplacian operator in both Euclidean and hyperbolic spaces. Assuming that the nonlinear…
Min-oo conjecture for fully nonlinear conformally invariant equations
Ezequiel Barbosa, Marcos P. Cavalcante, José M. Espinar
In this paper we show rigidity results for super-solutions to fully nonlinear elliptic conformally invariant equations on subdomains of the standard -sphere under…
Halfspace type Theorems for Self-Shrinkers
Marcos P. Cavalcante, Jose M. Espinar
In this short paper we extend the classical Hoffman-Meeks Halfspace Theorem to self-shrinkers, that is: "Let be a hyperplane passing through the origin. The only properly imme…
Examples and structure of CMC surfaces in some Riemannian and Lorentzian homogeneous spaces
Marcos P. de A. Cavalcante, Jorge H. S. de Lira
It is proved that the holomorphic quadratic differential associated to CMC surfaces in Riemannian products $\mathbb{S}^2\times\Rr$ and $\mathbb{H}^2\times \Rr$ discovered by U. Abr…