Publications

• R. Batista, A. Lima, P. Sousa and B. Vieira, Area-charge inequalities and rigidity of non-time-symmetric initial data sets. preprint.

• R. Batista, A. Lima and P. Sousa, Some results on  $\mathfrak{g}$-stability for hypersurfaces in an initial data set. Nonlinear Analysis, v. 262, p.113914, 2026. journal

• R. Batista, A. Lima and P. Sousa, Rigidity of marginally outer trapped surfaces in charged initial data sets. Letters in Mathematical in Physics. Vol.145, 41, 2025. journal

• R. Batista and L. Lima, A harmonic level set proof of a positive mass theorem. Proceedings of the American Mathemathical Society. Vol. 153, nº 4, p. 1761-1770, 2025. journal

• R. Batista, B. Lima and J. Silva, Rigidity of free boundary minimal disks in mean convex three-manifolds. The Journal of Geometric Analysis. Vol. 34, 279, 2024. journal

• A. Barros, H. Baltazar and R. Batista, A local rigidity theorem for minimal two-spheres in charged time-symmetric initial data set. Let. Math. Phys. Vol. 113, 92, 2023. journal

• R. Batista, B. Lima, P. Sousa and B. Vieira, Estimates for the  first fourth Steklov eigenvalue of  a minimal hypersurface with free boundary. Pacific J. Math. Vol. 325, nº 1, 2023. journal

• R. Batista, B. Lima,  P. Sousa and B. Vieira, Rigidity of capillary surfaces in compact 3-manifolds with strictly convex boundary. Proc. Edinb. Math. Soc. Vol. 66, p. 231-240, 2023. journal

• H. Baltazar, R. Batista and K. Bezerra, On the volume functional of compact manifolds with boundary with harmonic Weyl tensor. Mathematische Nachrichten. Vol 296, 2023. journal  

• H. Baltazar, R. Batista and E. Ribeiro Jr., Geometric inequalities for critical metrics of the volume functional. Annali di Matematica Pura ed Applicata. Vol. 201, p.1463-1480, 2022. journal

• R. Batista, M. Ranieri and E. Ribeiro Jr., Remarks on complete noncompact Einstein warped products. Communications in Analysis and Geometry. Vol. 28, p. 547-563, 2020. journal

• H. Baltazar, A. Barros, R. Batista and E. Viana, On static manifolds and related critical spaces with zero radial Weyl curvature. Monatshefte fur Mathematik.  Vol. 191, p. 449, 2020. journal

• A. Barros, R. Batista and P. Sousa, A new class of Killing Invariant Surfaces in 𝕊3. International Journal of Mathematics. Vol. 29, p. 1-11, 2018. journal

• A. Barros, R. Batista and C. Cruz, Hawking mass and local rigidity of minimal surfaces in three-manifolds. Communications in Analysis and Geometry. Vol. 25, p. 1-23, 2017. journal

• R. Batista, R. Diógenes, M. Ranieri and Ernani Jr., Critical metrics of the volume functional on compact three-manifolds with smooth boundary. J. Geom. Anal. V. 27, 2017. journal

• R. Batista and A.W. Cunha, Estimates of the first Steklov eigenvalue of properly embedded minimal hypersurfaces with free boundary. Bull. Braz. Math. Soc. Vol. 47, p. 871-881, 2016. journal  

• A. Barros, R. Batista, C. Cruz and P. Sousa, Rigidity in dimension four of area-minimising Einstein manifolds. Math. Proc. Cambridge Philos. Soc. (Print). Vol. 158, p. 355-363, 2015.  journal 

• A. Barros, R. Batista and E. Ribeiro Jr., Bounds on volume growth of geodesic balls for Einstein warped products. Proc. Amer. Math. Soc. Vol. 143, p. 4415-4422, 2015. journal 

• A. Barros, R. Batista and E. Ribeiro Jr., Compact almost Ricci solitons with constant scalar curvature are gradient. Monatshefte fur Mathematik (Print). Vol. 174, p. 29-39, 2014. journal

•  A. Barros, R. Batista and E. Ribeiro Jr., Rigidity of gradient almost Ricci solitons. Illinois Journal of  Mathematics. Vol. 56, p. 1267-1279, 2012. journal