H. Alencar

activity

20092026

most citedEigenvalue estimates for a class of elliptic differential operators on compact manifolds

9 citations · 21 across the 20 of their papers we have counts for

collaborators

22 papers

math.DG2026

Asymptotically conical shrinking ends of the $r$ -mean curvature flow: rotational construction and uniqueness

Hilário Alencar, Márcio Batista, Gregório Silva Neto

For $1 \leq r \leq n - 1$ we study shrinking self-similar ends of the $r$ -mean curvature flow, $S_{r} = c ⟨ X, N ⟩$ with $c < 0$ , that are asymptotic to a cone. For every rotational…

math.DG2026

An Abresch-Rosenberg type tensor and a gap theorem for CMC hypersurfaces in $S^{n} \times R$ and $H^{n} \times R$

Hilário Alencar, Márcio Batista, Harold Rosenberg

We construct a symmetric trace-free tensor for constant-mean-curvature hypersurfaces in $S^{n} \times R$ and $H^{n} \times R$ that extends the Abresch-R…

math.DG2026

Spheres under a Cauchy-Riemann inequality in $E (κ, τ)$ , and non-CMC Hopf tori

Hilário Alencar, Harold Rosenberg

For a smooth, connected, oriented surface $Σ$ , topologically a sphere, immersed in the homogeneous space $E (κ, τ)$ with $τ \neq = 0$ , we show that a one-sided Cauchy--Riemann-type inequa…

math.DG2026

Half-space theorems for translating solitons of the r-mean curvature flow

Hilário Alencar, G. Pacelli Bessa, Gregório Silva Neto

In this paper, we establish nonexistence results for complete translating solitons of the r-mean curvature flow under suitable growth conditions on the (r-1)-mean curvature and on…

math.DG2024

Gap theorems for complete self-shrinkers of $r$ -mean curvature flows

Hilário Alencar, G. Pacelli Bessa, Gregório Silva Neto

In this paper, we prove gap results for complete self-shrinkers of the $r$ -mean curvature flow involving a modified second fundamental form. These results extend previous results f…

math.DG2024

On $O (p) \times O (q)$ -invariant constant mean curvature hypersurfaces with singularity

Hilário Alencar, Ronaldo Garcia, Gregório Silva Neto

We classify the $O (p) \times O (q)$ -invariant constant mean curvature hypersurfaces with singularity at the origin, solving a conjecture of Wu-yi Hsiang.

math.DG2022

On the spectrum and index of expanding and translating solitons of the mean curvature flow in $R^{3}$

Hilário Alencar, Gregório Silva Neto

In this paper we prove that two-dimensional translating solitons in $R^{3}$ with finite $L$ -index are homeomorphic to a plane or a cylinder and that a two-dimensional self-e…

math.DG2022

Hopf type theorems in Riemannian manifolds

Hilário Alencar, Gregório Silva Neto, Detang Zhou

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. In this paper w…

math.DG2022

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…

math.DG2022

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…

math.DG2021

Stability properties of complete self-shrinking surfaces in $R^{3}$

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 $R^{3} .$ We prove that an immersed se…

math.DG2020

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…

math.DG2020

Hopf type theorems for self-similar solutions of curvature flows in $R^{3}$

Hilário Alencar, Gregório Silva Neto, Detang Zhou

In this paper we prove rigidity results for two-dimensional, closed, immersed, non-necessarily convex, self-similar solutions of a wide class of fully non-linear parabolic flows in…

math.DG2020★ 3 cited

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…

math.DG2017

The $f$ -Stability Index of the Constant Weighted Mean Curvature Hypersurfaces in Gradient Ricci Solitons

Hilário Alencar, Adina Rocha

In this paper, we prove that a noncompact complete hypersurface with finite weighted volume, weighted mean curvature vector bounded in norm, and isometrically immersed in a complet…

math.DG2016★ 2 cited

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…

math.DG2015★ 2 cited

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…

math.DG2015

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…

math.DG2015★ 1 cited

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…

math.DG2013★ 9 cited

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 $…

math.DG2009★ 1 cited

Stable hypersurfaces with constant scalar curvature in Euclidean spaces

Hilário Alencar, Walcy Santos, Detang Zhou

We obtain some nonexistence results for complete noncompact stable hyppersurfaces with nonnegative constant scalar curvature in Euclidean spaces. As a special case we prove that th…

math.DG2009★ 3 cited

Curvature integral estimates for complete hypersurfaces

Hilário Alencar, Walcy Santos, Detang Zhou

We consider the integrals of $r$ -mean curvatures $S_{r}$ of a complete hypersurface $M$ in space forms $Q_{c}^{n + 1}$ which generalize volume $(r = 0)$ , total mean curvature $(r…

Asymptotically conical shrinking ends of the r-mean curvature flow: rotational construction and uniqueness

An Abresch-Rosenberg type tensor and a gap theorem for CMC hypersurfaces in Sn×R and Hn×R

Spheres under a Cauchy-Riemann inequality in E(κ,τ), and non-CMC Hopf tori

Half-space theorems for translating solitons of the r-mean curvature flow

Gap theorems for complete self-shrinkers of r-mean curvature flows

On O(p)×O(q)-invariant constant mean curvature hypersurfaces with singularity

On the spectrum and index of expanding and translating solitons of the mean curvature flow in R3

Hopf type theorems in Riemannian manifolds

Hopf type theorems for surfaces in the de Sitter-Schwarzschild and Reissner-Nordstrom manifolds

Poincaré type inequality for hypersurfaces and rigidity results

Stability properties of complete self-shrinking surfaces in R3

Rigidity of complete self-shrinkers whose tangent planes omit a nonempty set

Hopf type theorems for self-similar solutions of curvature flows in R3

Hopf type Theorem for Self-Shrinkers

The f-Stability Index of the Constant Weighted Mean Curvature Hypersurfaces in Gradient Ricci Solitons

Isoperimetric inequalities and monotonicity formulas for submanifolds in warped product manifolds

Stable hypersurfaces with zero scalar curvature in Euclidean space

Monotonicity formula for complete hypersurfaces in the Hyperbolic space and applications

Poincaré and mean value inequalities for hypersurfaces in Riemannian manifolds and applications

Eigenvalue estimates for a class of elliptic differential operators on compact manifolds

Stable hypersurfaces with constant scalar curvature in Euclidean spaces

Curvature integral estimates for complete hypersurfaces

Asymptotically conical shrinking ends of the $r$ -mean curvature flow: rotational construction and uniqueness

An Abresch-Rosenberg type tensor and a gap theorem for CMC hypersurfaces in $S^{n} \times R$ and $H^{n} \times R$

Spheres under a Cauchy-Riemann inequality in $E (κ, τ)$ , and non-CMC Hopf tori

Gap theorems for complete self-shrinkers of $r$ -mean curvature flows

On $O (p) \times O (q)$ -invariant constant mean curvature hypersurfaces with singularity

On the spectrum and index of expanding and translating solitons of the mean curvature flow in $R^{3}$

Stability properties of complete self-shrinking surfaces in $R^{3}$

Hopf type theorems for self-similar solutions of curvature flows in $R^{3}$

The $f$ -Stability Index of the Constant Weighted Mean Curvature Hypersurfaces in Gradient Ricci Solitons