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On regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces
Alexandre Paiva Barreto, Francisco Fontenele, Luiz Hartmann
We prove that there are no regular algebraic hypersurfaces with non-zero constant mean curvature in the Euclidean space , , defined by polynomials of odd…
A conformal characterization of manifolds of constant sectional curvature
Xiaoyang Chen, Francisco Fontenele, Frederico Xavier
A special case of the main result states that a complete -connected Riemannian manifold is isometric to one of the models , , of…
Rotational Surfaces with second fundamental form of constant length
Alexandre P. Barreto, Francisco Fontenele, Luiz Hartmann
We obtain an infinite family of complete non embedded rotational surfaces in whose second fundamental forms have length equal to one at any point. Also we prove that…
Good shadows, dynamics, and convex hulls
Francisco Fontenele, Frederico Xavier
The Ekeland variational principle implies what can be regarded as a strong version, in the category, of the Yau minimum principle: under the appropriate hypotheses {\it every…
A Riemannian Bieberbach estimate
Francisco Fontenele, Frederico Xavier
The Bieberbach estimate, a pivotal result in the classical theory of univalent functions, states that any injective holomorphic function on the open unit disc satisfies $|f…
Heinz type estimates for graphs in Euclidean space
Francisco Fontenele
Let be the graph of a -real valued function defined in a closed ball of . In this work, we obtain upper bounds for and $\i…