4 papers
Half-space theorems for -surfaces of
G. Pacelli Bessa, Tiarlos Cruz, Leandro F. Pessoa
In this paper we investigate the intersection problem for -surfaces immersed in a complete Riemannian three-manifold with Ricci curvature bounded from below by . We firs…
Critical metrics and curvature of metrics with unit volume or unit area of the boundary
Tiarlos Cruz, Almir Silva Santos
Given a smooth compact manifold with boundary, we study variational properties of the volume functional and of the area functional of the boundary, restricted to the space of the R…
On the prescribed -curvature problem in Riemannian manifolds
Flávio França Cruz, Tiarlos Cruz
We prove the existence of metrics with prescribed -curvature under natural assumptions on the sign of the prescribing function and the background metric. In the dimension four c…
Prescribing the curvature of Riemannian manifolds with boundary
Tiarlos Cruz, Feliciano Vitório
Let be a compact connected surface with boundary. We prove that the signal condition given by the Gauss-Bonnet theorem is necessary and sufficient for a given smooth function $…