arXiv subjects

Feliciano Vitorio

Publications and source records attributed to Feliciano Vitorio.

7 recordsLinked to original sources

arXiv2016

Hardy and Rellich Inequalities for submanifolds in Hadamard spaces

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 by Michael-Simon and Hoffman-Spruck. Since then, a sort of applications to the submanifold theory has been derived from those inequalities. Years later, Carron obtained a Hardy inequality for submanifolds in Hadamard spaces. In this paper, we prove the general Hardy and Rellich Inequalities for submanifolds in Hadamard spaces. Some applications are given and we also analyse the equality cases.

math.DG↗

arXiv2015

Einstein $4-$Manifolds and Nonpositive Isotropic Curvature

This note is devoted to study the implications of nonpositive isotropic curvature and negative Ricci curvature for Einstein $4-$Manifolds.

math.DG↗

arXiv2014

Rigidity Theorems of conformal class on compact manifolds with boundary

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 integral conditions on the the scalar curvatures and the mean curvatures on the boundary. No condition on the first eigenvalues of operators is need.

math.DG↗

arXiv2014

Global isometric embeddings of multiple warped product metrics into quadrics

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 given by Blanusa, Rozendorn, Henke and Azov.

math.DG↗

arXiv2013

The non-parabolicity of infinite volume ends

Let $M^m$, with $m\geq 3$, be an $m$-dimensional complete noncompact manifold isometrically immersed in a Hadamard manifold $\bar M$. Assume that the mean curvature vector has finite $L^p$-norm, for some $2\leq p\leq m$. We prove that each end of $M$ must either have finite volume or be non-parabolic.

math.DG↗

arXiv2013

The positive mass Theorem and Penrose inequality for graphical manifolds

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 which includes, for instance, that ones with flat normal bundle.

math.DG↗

arXiv2012

L^2 Harmonic 1-forms on submanifolds with finite total curvature

Let $x:M^m\to \bar M$, with $m\geq 3$, be an isometric immersion of a complete noncompact manifold $M$ in a complete simply-connected manifold $\bar M$ with sectional curvature satisfying $-c^2\leq K_{\bar M}\leq 0$, for some constant $c$. Assume that the immersion has finite total curvature. If $c\neq 0$, assume further that the first eigenvalue of the Laplacian of $M$ is bounded from below by a suitable constant. We prove that the space of the $L^2$ harmonic 1-forms on $M$ has finite dimension. Moreover there exists a constant $\La>0$, explicitly computed, such that if the total curvature is bounded from above by $\La$ then there is no nontrivial $L^2$-harmonic 1-forms on $M$.

math.DG↗