I have been working on a variety of topics centering around global issues in Geometric Analysis, with a strong motivation coming from Mathematical Physics. In recent years, my reasearch interests are focused on the following subjects:

• Mathematical Relativity (mass, Penrose inequalities and black hole uniqueness for a large class of initial data sets);

• Probability Theory and its applications, including Stochastic Analysis (Feynman-Kac formulae for the heat semigroup of generalized Dirac Laplacians under mixed boundary conditions);

• Index Theory (as applied to finding obstructions to the existence of positive scalar curvature metrics on certain non-compact manifolds);

• Analysis on Singular Spaces (with an emphasis on mapping properties of the associated geometric operators). 

Most of my published papers, which are listed below, may be found in the online repository arXiv; see also my Google Scholar. Be aware, however, that the arXiv files may substantially differ from the published versions, which are listed in  Mathscinet (subscription required).

• (with L.P. Jorge) Local stability of the first eigenvalue of the Laplacian, Matemática Contemporânea, vol. 9, 111-116, 1995, SBM.  here

• (with W. Rossman) On the index of constant mean curvature 1 surfaces in hyperbolic space. Indiana Univ. Math. J. 47 (1998), no. 2, 685–723. here

• (with J.X. da Cruz Neto and P.R. Oliveira) Geodesic algorithms in Riemannian geometry. Balkan J. Geom. Appl. 3 (1998), no. 2, 89–100.  here

• (with J.F. Montenegro) Classification of solitons for the affine curvature flow. Comm. Anal. Geom. 7 (1999), no. 4, 731–753.  here

• (with  V.F. de Sousa Neto and W. Rossman) Lower bounds for index of Wente tori. Hiroshima Math. J. 31 (2001), no. 2, 183–199.  here

• (with P. Roitman) Constant mean curvature one surfaces in hyperbolic 3-space using the Bianchi-Calò method. An. Acad. Brasil. Ciênc. 74 (2002), no. 1, 19–24. 

• (with I.C. Lázaro) A Cauchy-Crofton formula and monotonicity inequalities for the Barbosa-Colares functionals. Asian J. Math. 7 (2003), no. 1, 81–89. here

• (with C. Barroso and W. Santos) Monotonicity inequalities for the r-area and a degeneracy theorem for r-minimal graphs. J. Geom. Anal. 14 (2004), no. 4, 557–566. here

• Infinite connected sums, K-area and positive scalar curvature, arXiv 

• (with J. Lira) The Christoffel problem in Lorentzian geometry. J. Inst. Math. Jussieu 5 (2006), no. 1, 81–99. here

• (with M.A. Javaloyes and P. Piccionne) Iteration of closed geodesics in stationary Lorentzian manifolds. Math. Z. 260 (2008), no. 2, 277–303. here

• (with N.L. Santos) Deformations of 2k-Einstein structures. J. Geom. Phys. 60 (2010), no. 9, 1279–1287. here

• (with J. Lira and J. Silva) New r-minimal hypersurfaces via perturbative methods. J. Geom. Anal. 21 (2011), no. 4, 1132–1156. here

• (with A. Sousa) Two-ended r-minimal hypersurfaces in Euclidean space. Illinois J. Math. 55 (2011), no. 4, 1327–1348 (2013). here

• (with P. Piccione and M. Zedda) On bifurcation of solutions of the Yamabe problem in product manifolds. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 2, 261–277. here

• (with P. Piccione and M. Zedda) A note on the uniqueness of solutions for the Yamabe problem. Proc. Amer. Math. Soc. 140 (2012), no. 12, 4351–4357.

• (with T. Caula and N.L. Santos) Deformation and rigidity results for the 2k-Ricci tensor and the 2k-Gauss-Bonnet curvature. Math. Nachr. 286 (2013), no. 17-18, 1752–1777. here

• (with J. Lira and P. Piccione) Bifurcation of Clifford tori in Berger 3-spheres. Q. J. Math. 65 (2014), no. 4, 1345–1362. here

• (with F. Girão) Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces. Gen. Relativity Gravitation 47 (2015), no. 3, Art. 23, 20 pp.  here

• (with F. Girão) The ADM mass of asymptotically flat hypersurfaces. Trans. Amer. Math. Soc. 367 (2015), no. 9, 6247–6266. here

• (with F. Girão) An Alexandrov-Fenchel-type inequality in hyperbolic space with an application to a Penrose inequality. Ann. Henri Poincaré 17 (2016), no. 4, 979–1002. here

• (with F. Girão, W. Lozório and J. Silva) Penrose inequalities and a positive mass theorem for charged black holes in higher dimensions. Classical Quantum Gravity 33 (2016), no. 3, 035008, 14 pp. here

• (with S. Almaraz and E. Barbosa) A positive mass theorem for asymptotically flat manifolds with a non-compact boundary. Comm. Anal. Geom. 24 (2016), no. 4, 673–715. here

• (with E. Barbosa and F. Girão) On the limiting behavior of the Brown-York quasi-local mass in asymptotically hyperbolic manifolds. Differential Geom. Appl. 53 (2017), 56–75. here

• A Feynman-Kac formula for differential forms on manifolds with boundary and geometric applications. Pacific J. Math. 292 (2018), no. 1, 177–201. arxiv, journal.

• (with C.T. Cruz and J.F. Montenegro) Deforming the scalar curvature of the de Sitter–Schwarzschild space. J. Geom. Anal. 28 (2018), no. 1, 473–491. arxiv, journal.

• Recurrence and transience for normally reflected Brownian motion in warped product manifolds. Stoch. Dyn. 19 (2019), no. 2, 1950013, 14 pp.  arxiv, journal.

• (with F. Girão and A. Montalbán) The mass in terms of Einstein and Newton. Classical Quantum Gravity 36 (2019), no. 7, 075017, 11 pp.  arxiv, journal.

• A probabilistic proof of the Gauss-Bonnet formula for manifolds with boundary,  arxiv

• Heat conservation for generalized Dirac Laplacians on manifolds with boundary, Annali de Matematica Pura ed Aplicata, 199, 997–1021(2020) arxiv, journal

• (with E. Barbosa and A. Freitas) The generalized Pohozaev-Schoen identity and some geometric applications,  Comm. Analysis and Geometry, 28. vol. 2,  (2020)  223 – 242 , arxiv, journal

• (with S. Almaraz) The mass of an asymptotically hyperbolic manifold with a noncompact boundary, Ann. Henri Poincaré 21, 3727–3756 (2020) , arxiv, journal

• (with S. Almaraz and L. Mari) Spacetime positive mass theorems for initial data sets with noncompact boundary, International Mathematics Research Notices,, rnaa226, arXiv, journal

• (with S. ALmaraz) Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds, Calc. Var.  & PDEs, 62, 196 (2023), arXiv, journal.

• Conserved quantities in General Relativity: the case of initial data sets with a noncompact boundary, invited contribution appearing in "Perspectives in Scalar Curvature", edited by M. Gromov and H.B. Lawson, World Scientific (2022) arXiv, book, chapter

• The scalar curvature in conical manifolds: some results on existence and obstructions, Annals of Global Analysis and Geometry, 2022,  arXiv , journal

• (with F. Girão and J. Natário) Extrinsic black hole uniqueness in pure Lovelock gravity, Bullletin of BMS, 2021, arxiv, journal

• (with S. Almaraz) Rigidity of non-compact static domains in hyperbolic space via positive mass thorems, 2022, to appear in the Annali della Scuola Normale Superiore de Pisa, arxiv

• Mapping properties of geometric elliptic operators in conformally conical spaces: an introduction with examples, Matemática Contemporânea, 2022, arxiv, journal

• The scalar curvature in wedge spaces: existence and obstructions, 2023, arxiv

• Einstein-Yang-Mills fields in conformally compact manifolds, 2023, arxiv

• (with R. Batista) A harmonic level set proof of a positive mass theorem, arxiv