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math.DG2022
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…
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…