2 citations · 5 across the 11 of their papers we have counts for
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Hardy and Rellich Inequalities for submanifolds in Hadamard spaces
Marcio Batista, Heudson Mirandola, Feliciano Vitorio
Some of the most known integral inequalities are the Sobolev, Hardy and Rellich inequalities in Euclidean spaces. In the context of submanifolds, the Sobolev inequality was proved…
The Caffarelli-Kohn-Nirenberg Inequality for Submanifolds in Riemannian Manifolds
Márcio Batista, Heudson Mirandola, Feliciano Vitório
After works by Michael and Simon [10], Hoffman and Spruck [9], and White [14], the celebrated Sobolev inequality could be extended to submanifolds in a huge class of Riemannian man…
Rigidity Theorems of conformal class on compact manifolds with boundary
Ezequiel Barbosa, Heudson Mirandola, Feliciano Vitorio
Let M be a compact manifold with boundary. In this paper, we discuss some rigidity theorems of metrics in a same conformal class that fixes the boundary and satisfy certain integra…
Sobolev and isoperimetric inequalities for submanifolds in weighted ambient spaces
Marcio Batista, Heudson Mirandola
In this paper, we prove a Sobolev and isoperimetric inequalities for submanifold in weighted manifold. Our results generalize the Hoffman-Spruck's inequalities.
The positive mass Theorem and Penrose inequality for graphical manifolds
Heudson Mirandola, Feliciano Vitorio
We give, via elementary methods, explicit formulas for the ADM mass which allow us to conclude the positive mass theorem and Penrose inequality for a class of graphical manifolds w…
Global isometric embeddings of multiple warped product metrics into quadrics
Heudson Mirandola, Feliciano Vitorio
In this paper, we construct smooth isometric embeddings of multiple warped product manifolds in quadrics of semi-Euclidean spaces. Our main theorem generalizes previous results as…
Isometry actions and geodesics orthogonal to submanifolds
Antonio J. Di Scala, Sérgio Mendonça, Heudson Mirandola +1
We investigate submanifolds in space forms such that every geodesic orthogonal to the submanifold intersects a fixed totally geodesic submanifold. We obtain an application to horos…
Integral estimates for the trace of symmetric operators
Marcio Batista, Heudson Mirandola
Let be a positive-semidefinite symmetric operator of class defined on a complete non-compact manifold isometrically immersed in a Hadamard space . I…
The non-parabolicity of infinite volume ends
Marcos P. Cavalcante, Heudson Mirandola, Feliciano Vitorio
Let , with , be an -dimensional complete noncompact manifold isometrically immersed in a Hadamard manifold . Assume that the mean curvature vector has fini…
L^2 Harmonic 1-forms on submanifolds with finite total curvature
Marcos P. Cavalcante, Heudson Mirandola, Feliciano Vitorio
Let , with , be an isometric immersion of a complete noncompact manifold in a complete simply-connected manifold with sectional curvature sat…
Homotopy Groups, Focal Points and Totally Geodesic Immersions
Sérgio Mendonça, Heudson Mirandola
In this paper we consider on a complete Riemannian manifold an immersed totally geodesic hypersurface $\Si$ existing together with an immersed submanifold without focal poi…