arXiv subjects

Fábio Reis dos Santos

Publications and source records attributed to Fábio Reis dos Santos.

3 recordsLinked to original sources

arXiv2026

An integral inequality for compact Bach-flat $\mathcal{A}_{2}$-manifolds

We establish a Catino-type integral inequality for closed Bach-flat $\mathcal{A}_2$-manifolds, namely Riemannian manifolds with nonnegative scalar curvature and constant nonnegative second Schouten curvature. In the equality case, we derive rigidity results showing that the manifold is either Einstein or isometrically covered by $\mathbb{S}^{1}\times\mathbb{S}^{n-1}(κ)$ endowed with the product metric.

math.DG↗

arXiv2025

A Liouville-type theorem for the p-Laplacian on complete non-compact Riemannian manifolds

A Liouville-type result for the p-Laplacian on complete Riemannian manifolds is proved. As an application are present some results concerning complete non-compact hypersurfaces immersed in a suitable warped product manifold.

math.DG↗

arXiv2024

A remark on the first eigenvalue of the p-Laplacian on compact submanifolds in the unit sphere

An integral inequality for the singular p-laplacian is established for 3/2<p<2. As consequence, lower bounds for the first eigenvalue of the p-laplacian are obtained for minimal submanifolds and prescribed scalar curvature submanifolds in the unit sphere.

math.DG↗