5 citations · 25 across the 13 of their papers we have counts for
17 papers
On the fundamental tone of the -Laplacian on Riemannian manifolds and applications
Francisco G. de S. Carvalho, Marcos Petrucio Cavalcante
We present a general lower bound for the fundamental tone for the -Laplacian on Riemannian manifolds carrying a special kind of function. We then apply our result to the cases o…
Index bounds for closed minimal surfaces in 3-manifolds with the Killing property
Marcos P. Cavalcante, Darlan F. de Oliveira, Robson dos S. Silva
Let be a closed minimal surface immersed in a Riemannian 3-manifold carrying an orthonormal Killing frame. This class of ambient spaces includes Lie groups with a bi-invariant…
Gap phenomena for constant mean curvature surfaces
Ezequiel Barbosa, Marcos P. Cavalcante, Edno Pereira
In this paper, we prove gap results for constant mean curvature (CMC) surfaces. Firstly, we find a natural inequality for CMC surfaces which imply convexity for distance function.…
The halfspace theorem for minimal hypersurfaces in regions bounded by minimal cones
Marcos Petrúcio Cavalcante, Wagner Oliveira Costa-Filho
We prove that there are no minimal hypersurfaces properly immersed in any region of the Euclidean space bounded by unstable minimal cones. We also prove the analogous result for $r…
Vanishing theorems for the cohomology groups of free boundary hypersurfaces
Marcos P. Cavalcante, Abraão Mendes, Feliciano Vitório
In this paper, we prove that there exists a universal constant , depending only on positive integers and , such that if is a compact free boundary sub…
Index Estimates for Free Boundary Constant Mean Curvature Surfaces
Marcos P. Cavalcante, Darlan F. de Oliveira
In this paper, we consider compact free boundary constant mean curvature surfaces immersed in a mean convex body of the Euclidean space or in the unit sphere. We prove that the Mor…
Lower bounds for the index of compact constant mean curvature surfaces in and
Marcos P. Cavalcante, Darlan F. de Oliveira
Let be a compact constant mean curvature surface either in or . In this paper we prove that the stability index of is bounded below by a linear…
Uniqueness Theorems for fully nonlinear conformal equations on subdomains of the sphere
Marcos P. Cavalcante, José M. Espinar
In this paper we prove classification results to elliptic fully nonlinear conformal equations on certain subdomains of the sphere with prescribed constant mean curvature on its bou…
Constant Mean Curvature Surfaces in and Finite Total Curvature
Márcio Batista, Marcos P. Cavalcante, Dorel Fetcu
We consider surfaces with parallel mean curvature vector field and finite total curvature in product spaces of type , where is a…
Some Isoperimetric Inequalities and Eigenvalue Estimates in Weighted Manifolds
Marcio Batista, Marcos P. Cavalcante, Juncheol Pyo
In this paper we prove general inequalities involving the weighted mean curvature of compact submanifolds immersed in weighted manifolds. As a consequence we obtain a relative line…
On the fundamental tone of immersions and submersions
Marcos Petrúcio Cavalcante, Fernando Manfio
In this paper we obtain lower bound estimates of the spectrum of Laplace-Beltrami operator on complete submanifolds with bounded mean curvature, whose ambient space admits a Rieman…
The p-Hyperbolicity of Infinity Volume Ends and Applications
Marcio Batista, Marcos Petrucio Cavalcante, Newton Santos
In this paper we prove a characterization of -hyperbolic ends on complete Riemannian manifolds which carries a Sobolev type inequality.
The non-parabolicity of infinite volume ends
Marcos P. Cavalcante, Heudson Mirandola, Feliciano Vitorio
Let , with , be an -dimensional complete noncompact manifold isometrically immersed in a Hadamard manifold . Assume that the mean curvature vector has fini…
L^2 Harmonic 1-forms on submanifolds with finite total curvature
Marcos P. Cavalcante, Heudson Mirandola, Feliciano Vitorio
Let , with , be an isometric immersion of a complete noncompact manifold in a complete simply-connected manifold with sectional curvature sat…
Stability Properties of Rotational Catenoids in the Heisenberg Groups
Pierre Bérard, Marcos P. Cavalcante
In this paper, we determine the maximally stable, rotationally invariant domains on the catenoids $\cC_a$ (minimal surfaces invariant by rotations) in the Heisenberg group with a l…
Eigenvalue estimates for hypersurfaces in and applications
Pierre Bérard, Philippe Castillon, Marcos P. Cavalcante
In this paper, we give a lower bound for the spectrum of the Laplacian on minimal hypersurfaces immersed into . As an application, in dimension 2, we prove that a com…
Convexity in locally conformally flat manifolds with boundary
Marcos P. Cavalcante
Given a closed subset $\La$ of the open unit ball , , we will consider a complete Riemannian metric on $\bar{B_1} \setminus \La$ of constant scala…