Publications

Selected Papers

• Integral and boundary estimates for critical metrics of the volume functional. To appear in  Israel J. Mathematics, (2023) (with R. Diógenes and N. Pinheiro).

• Geometry of static perfect fluid space-time. Classical and Quantum Gravity, 40 (2023) 205012 (with J. Costa, R. Diógenes and N. Pinheiro)

• On Euler characteristic and Hitchin-Thorpe inequality for four-dimensional compact Ricci solitons. Proc. Amer. Math. Soc. 10 (2023) 33-45 (with X. Cheng and D. Zhou).

• Geometry of compact quasi-Einstein manifolds with boundary.  Manuscripta Math.  169 (2022) 167 - 183 (with R. Diógenes and T. Gadelha).

• Geometric inequalities for critical Metrics of the volume functional. Annali di Matematica Pura ed Appl. 201 (2022) 1463–1480 (with H. Baltazar and R. Batista).

• Volume growth estimates for Ricci solitons and quasi-Einstein manifolds. J. Geom. Analysis, 32 (2022) p. 62. (with X. Cheng and D. Zhou). 

• Remarks on compact quasi-Einstein manifolds with boundary. Proc. Amer. Math. Soc. 150 (2022) 351-363. (with R. Diógenes and T. Gadelha).

• Four-dimensional complete gradient shrinking Ricci solitons. J. Reine Angew. Math. (Crelle's  Journal) 778 (2021) 127-144. (with H.-D. Cao and D. Zhou).

• Volume functional of compact manifolds with a prescribed boundary metric. J. Geom. Analysis, 31 (2021) 4703 - 4720. (with H. Baltazar and R. Diógenes).

• Noncompact quasi-Einstein manifolds conformal to a Euclidean space. Math. Nachr. 294 (2021) 132 - 144. (with K. Tenenblat).

• Remarks on complete noncompact Einstein warped products. Comm. Analysis and Geometry, v. 28, n. 3 (2020) 549-565. (with R. Batista and M. Ranieri).

• Static perfect fluid space-time on compact manifolds. Classical and Quantum Gravity, 37 (2020) 015003. (with F. Coutinho, R. Diógenes and B. Leandro).

• Isoperimetric inequality and Weitzenböck type formula for critical metrics of the volume. Israel J. Mathematics, v. 234, p. 309-329 (2019). (with Baltazar and Diógenes)

• Four-dimensional manifolds with pinched positive sectional curvature. Geometriae Dedicata, 200 (2019) 321-330. (with R. Diógenes).

• Minimal volume invariants, topological sphere theorems and biorthogonal curvature on 4-manifolds. Math. Nachr. 292 (2019) 556-572. (with E. Costa).

• Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary, Pacific J. Math. 297 (2018) 29-45. (with H. Baltazar).

• Critical metrics of the volume functional on compact three-manifolds with smooth boundary, J. Geom. Analysis, 27 (2017) 1530-1547. (with R. Batista, R. Diógenes and M. Ranieri).

• Critical Metrics of the Volume Functional on Manifolds with Boundary, Proc. Amer. Math. Soc. 145 (2017) 3513-3523. (with H. Baltazar).

• Rigidity of four-dimensional compact manifolds with harmonic Weyl tensor, Annali di Matematica Pura ed Appl., 195 (6) (2016) 2171-2181.

• Bach-flat critical metrics of the volume functional on 4-dimensional manifolds with boundary, J. Geom. Analysis, 25 (2015) 2698-2715. (with A. Barros and R. Diógenes).

• Bounds on volume growth of geodesic balls for Einstein warped products, Proc. Amer. Math. Soc. 143 (2015) 4415-4422. (with A. Barros and R. Batista). 

• Four-dimensional compact manifolds with nonnegative biorthogonal curvature, Michigan Math. J. v. 63, p. 747-761, (2014). (with E. Costa). 

• Critical point equation on four-dimensional compact manifolds, Math. Nachr., v. 287, p. 1618-1623, (2014). (with A. Barros). 

• Some characterizations for compact almost Ricci solitons, Proc. Amer. Math. Soc. v.140, p.1033 -1040, (2012). (with A. Barros).

Preprints

• Rigidity of four-dimensional Kähler-Ricci solitons, ArXiv:2212.05267 [math.DG] (2022). (with X. Cao and H. Tran)

• Rigidity of compact quasi-Einstein manifolds with boundary. ArXiv:2401.16929 [math.DG] (2024). (with J. Costa and D. Zhou)