8 citations · 8 across the 12 of their papers we have counts for
15 papers
Band Width Estimates and Rigidity of Manifolds with Negative Curvature
Tiarlos Cruz
We establish optimal Lipschitz lower bounds for proper smooth functions on three-dimensional Riemannian manifolds with Ricci curvature bounded below by negative constants, yielding…
Conformal Geometry and Spectral Bounds on Manifolds with Boundary
Tiarlos Cruz, Leandro F. Pessoa, Erisvaldo Véras
This work investigates upper bounds for the spectrum of the Steklov-type operator on Riemannian manifolds with boundary. We extend the Fraser-Schoen estimate for the first positive…
Area-charge inequalities and rigidity of time-symmetric initial data sets
Tiarlos Cruz, Abraão Mendes
In this paper, we establish new area-charge inequalities for the boundary of time-symmetric Einstein-Maxwell initial data sets, in both compact and noncompact cases, under the domi…
Exploring light propagation in nonlinear electrodynamics: phase and group velocities and related phenomena
T. W. Cruz, V. A. De Lorenci, E. Guzmán-Herrera +1
Nonlinear electrodynamics has been an important area of research for a long time. Investigations based on nonlinear Lagrangians, such as Euler-Heisenberg and Born-Infeld, are instr…
Curvature Deformations on Complete Manifolds with Boundary
Tiarlos Cruz, Almir Silva Santos
This paper investigates conformal deformations of the scalar curvature and mean curvature on complete Riemannian manifolds with boundary. We establish sufficient conditions for the…
Blow-up analysis of Large conformal metrics with prescribed Gaussian and geodesic curvatures
Rayssa Caju, Tiarlos Cruz, Almir Silva Santos
Consider a compact Riemannian surface with nonempty boundary and negative Euler characteristic. Given two smooth non-constant functions in and in w…
On static manifolds satisfying an overdetermined Robin type condition on the boundary
Tiarlos Cruz, Ivaldo Nunes
In this work, we consider static manifolds with nonempty boundary . In this case, we suppose that the potential also satisfies an overdetermined Robin type cond…
Existence and obstructions for the curvature on compact manifolds with boundary
Tiarlos Cruz, Almir Silva Santos, Feliciano Vitório
We study the set of curvature functions which a given compact manifold with boundary can possess. First, we prove that the sign demanded by the Gauss-Bonnet Theorem is a necessary…
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…
On the -curvature and volume of compact manifolds
Maria Andrade, Tiarlos Cruz, Almir Silva Santos
In this work we are interested in studying deformations of the -curvature and the volume. For closed manifolds, we relate critical points of the total -curvature function…
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…
Min-max minimal surfaces, horizons and electrostatic systems
Tiarlos Cruz, Vanderson Lima, Alexandre de Sousa
We present a connection between minimal surfaces of index one and General Relativity. First, we show that for a certain class of (electro)static systems, each of its unstable horiz…
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 $…
Capacity inequalities and rigidity of cornered/conical manifolds
C. Tiarlos Cruz
We prove capacity inequalities involving the total mean curvature of hypersurfaces with boundary in convex cones and the mass of asymptotically flat manifolds with non-compact boun…