My research interests are mainly in Differential Geometry and its relationship with Partial Differential Equations, including conformal deformations of Riemannan manifolds and General Relativity.
My publications and preprints:
Rigidity of non-compact static domains in hyperbolic space via positive mass theorems (with Levi de Lima), to appear on Annali della Scuola Normale Superiore di Pisa (Classe di Scienze), https://doi.org/10.2422/2036-2145.202301_005.pdf
A priori estimates for negative constant scalar curvature conformal metrics with positive constant boundary mean curvature (with Shaodong Wang), Journal of the London Mathematical Society, 111:3 (2025), e70109. https://doi.org/10.1112/jlms.70109
A compactness theorem for conformal metrics with constant scalar curvature and constant boundary mean curvature in dimension three (with Shaodong Wang), Calc. Var. PDEs,64, 35 (2025). https://doi.org/10.1007/s00526-024-02895-2
A singular Yamabe problem on manifolds with solid cones (with Juan Alcon Apaza), Advances in Calculus of Variations, 17 (2024) 1131-1160. https://doi.org/10.1515/acv-2022-0105.pdf
Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds (with Levi de Lima), Calc. Var. PDEs, 62 (2023), 196, https://doi.org/10.1007/s00526-023-02519-1.pdf
Energy bounds of sign-changing solutions to Yamabe equations on manifolds with boundary (with Shaodong Wang), Nonlinear Analysis, 225 (2022), 113131, https://doi.org/10.1016/j.na.2022.113131.pdf
Spacetime positive mass theorems for initial data sets with noncompact boundary (with Levi de Lima and Luciano Mari). International Mathematics Research Notices, 2021:4 (2021) 2783–2841, https://doi.org/10.1093/imrn/rnaa226 .pdf
The mass of an asymptotically hyperbolic manifold with a noncompact boundary (with Levi de Lima). Annales Henri Poincaré, 21:11 (2020) 3727-3756, https://doi.org/10.1007/s00023-020-00954-w.pdf
Convergence of the Yamabe flow on manifolds with minimal boundary (with Liming Sun). Annali della Scuola Normale Superiore di Pisa (Classe di Scienze), 20:3 (2020) 1197-1272, https://doi.org/10.2422/2036-2145.201608_001.pdf
A compactness theorem for scalar-flat metrics on 3-manifolds with boundary (with Olivaine de Queiroz and Shaodong Wang). Journal of Functional Analysis 277:7 (2019) 2092-2116, https://doi.org/10.1016/j.jfa.2019.01.001.pdf
A remark on an eigenvalue problem with mixed boundary condition (with Ezequiel Barbosa). pre-print .pdf
A positive mass theorem for asymptotically flat manifolds with a non-compact boundary (with Ezequiel Barbosa and Levi de Lima). Commun. Anal. Geom., 24:4 (2016) 673-715, https://dx.doi.org/10.4310/CAG.2016.v24.n4.a1.pdf
Convergence of scalar-flat metrics on manifolds with boundary under a Yamabe-type flow. Journal of Diff. Equations, 259 (2015) 2626-2694 .pdf (Appendix B of this version contains more details than the published one.)
The asymptotic behavior of Palais-Smale sequences on manifolds with boundary, Pacific J. Math., 269:1 (2014) 1-17.pdf
Blow-up phenomena for scalar-flat metrics on manifolds with boundary, Journal of Diff. Equations, 251 (2011) 1813-1840 .pdf (This is a more detailed version.)
A compactness theorem for scalar-flat metrics on manifolds with boundary, Calc. Var. PDEs, 41:3 (2011) 341-386 .pdf
An existence theorem of conformal scalar-flat metrics on manifolds with boundary, Pacific J. Math. 248:1 (2010) 1-22 .pdf
Some talks I presented:
“Teoremas de massa positiva e problemas do tipo Yamabe” (in Portuguese). Seminário de EDP e Matemática Aplicada, video
“Spacetime positive mass theorems for initial data sets with noncompact boundary”. Workshop on Submanifold Theory and Geometric Analysis. Universidade Federal de São Carlos (Brazil), 2019: video
“The mass of asymptotically hyperbolic manifolds with non-compact boundary”. 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Taipei (Taiwan), 2018: slides
“On Yamabe-type problems on manifolds with boundary”. Mathematical Congress of the Americas (MCA), Montreal (Canada), 2017: slides ; 31st Brazilian Mathematics Colloquium, IMPA, Rio de Janeiro (Brazil), 2017: video
“Convergence of the Yamabe flow on manifolds with minimal boundary”. VI Workshop on Differential Geometry, Maceió (Brazil), 2016: video part 1 , video part 2
“A positive mass theorem for asymptotically flat manifolds with a noncompact boundary and an application to a Yamabe-type flow”. Differential Geometry & Geometric Analysis Seminar, Princeton University (USA), 2015: slides
“Convergence of a Yamabe-type flow for manifolds with boundary”. Second Pacific Rim Mathematical Association Congress (PRIMA), Shanghai (China), 2013: slides
“The set of conformal scalar-flat metrics on manifolds with boundary: compactness and noncompactness results”. 28th Brazilian Mathematics Colloquium, IMPA, Rio de Janeiro (Brazil), 2011: slides
