6 papers · 1 filter
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…