9 citations · 22 across the 16 of their papers we have counts for
17 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…
Gap theorems for complete self-shrinkers of -mean curvature flows
Hilário Alencar, G. Pacelli Bessa, Gregório Silva Neto
In this paper, we prove gap results for complete self-shrinkers of the -mean curvature flow involving a modified second fundamental form. These results extend previous results f…
On -invariant constant mean curvature hypersurfaces with singularity
Hilário Alencar, Ronaldo Garcia, Gregório Silva Neto
We classify the -invariant constant mean curvature hypersurfaces with singularity at the origin, solving a conjecture of Wu-yi Hsiang.
Classification of ruled surfaces as homothetic self-similar solutions of the inverse mean curvature flow in the Lorentz-Minkowski 3-space
Gregório Silva Neto, Vanessa Silva
In this paper, we classify the nondegenerate ruled surfaces in the three-dimensional Lorentz-Minkowski space that are homothetic self-similar solutions for the inverse mean curvatu…
Ruled surfaces as translating solitons of the inverse mean curvature flow in the three-dimensional Lorentz-Minkowski space
Gregório Silva Neto, Vanessa Silva
In this paper, we classify the nondegenerate ruled surfaces in the three-dimensional Lorentz-Minkowski space that are translating solitons for the inverse mean curvature flow. In p…
On the spectrum and index of expanding and translating solitons of the mean curvature flow in
Hilário Alencar, Gregório Silva Neto
In this paper we prove that two-dimensional translating solitons in with finite -index are homeomorphic to a plane or a cylinder and that a two-dimensional self-e…
Hopf type theorems for surfaces in the de Sitter-Schwarzschild and Reissner-Nordstrom manifolds
Hilário Alencar, Gregório Silva Neto
In 1951, H. Hopf proved that the only surfaces, homeomorphic to the sphere, with constant mean curvature in the Euclidean space are the round (geometrical) spheres. These results w…
Poincaré type inequality for hypersurfaces and rigidity results
Hilário Alencar, Márcio Batista, Gregório Silva Neto
In this article, under mild constraints on the sectional curvature, we exploit a divergence formula for symmetric endomorphisms to deduce a general Poincaré type inequality. We app…
Stability properties of complete self-shrinking surfaces in
Hilário Alencar, Gregório Silva Neto, Detang Zhou
This paper studies rigidity for immersed self-shrinkers of the mean curvature flow of surfaces in the three-dimensional Euclidean space We prove that an immersed se…
Rigidity of complete self-shrinkers whose tangent planes omit a nonempty set
Hilário Alencar, Manuel Cruz, Gregório Silva Neto
In this paper we prove rigidity results for the sphere, the plane and the right circular cylinder as the only self-shrinkers satisfying a classic geometric assumption, namely the u…
Hopf type Theorem for Self-Shrinkers
Hilário Alencar, Gregório Silva Neto, Detang Zhou
In this paper, we prove that a two-dimensional self-shrinker, homeomorphic to the sphere, immersed in the three dimensional Euclidean space is a round sphere, provided its mean cur…
Isoperimetric inequalities and monotonicity formulas for submanifolds in warped product manifolds
Hilário Alencar, Gregório Silva Neto
In this paper we first prove some linear isoperimetric inequalities for submanifolds in the de Sitter-Schwarzschild and Reissner-Nordstrom manifolds. Moreover, the equality is atta…
Stable hypersurfaces with zero scalar curvature in Euclidean space
Hilário Alencar, Manfredo do Carmo, Gregório Silva Neto
In this paper we prove some results concerning stability of hypersurfaces in the four dimensional Euclidean space with zero scalar curvature. First we prove there is no complete st…
Monotonicity formula for complete hypersurfaces in the Hyperbolic space and applications
Hilário Alencar, Gregório Silva Neto
In this paper we prove a monotonicity formula for the integral of the mean curvature for complete and proper hypersurfaces of the hyperbolic space and, as consequences, we obtain a…
Poincaré and mean value inequalities for hypersurfaces in Riemannian manifolds and applications
Hilário Alencar, Gregório Silva Neto
In the first part of this paper we prove some new Poincaré inequalities, with explicit constants, for domains of any hypersurface of a Riemannian manifold with sectional curvatures…
On Stable Hypersurfaces with Vanishing Scalar Curvature
Gregório Silva Neto
We will prove that \emph{there are no stable complete hypersurfaces of with zero scalar curvature, polynomial volume growth and such that …
Eigenvalue estimates for a class of elliptic differential operators on compact manifolds
Hilário Alencar, Gregório Silva Neto, Detang Zhou
The motivation of this paper is to study a second order elliptic operator which appears naturally in Riemannian geometry, for instance in the study of hypersurfaces with constant $…