Abraão Mendes

abraao.mendes@im.ufal.br
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Preprint

  1. Area-charge inequality and local rigidity in charged initial data sets. Preprint (2025). arXiv:2505.20060 PDF
  2. Rigidity of surfaces with nonpositive Euler characteristic by the second eigenvalue of the Jacobi operator. Preprint (2025). (com M. Batista, M.P. Cavalcante e I. Nunes) PDF
  3. Rigidity results for free boundary hypersurfaces in initial data sets with boundary. Preprint (2025). arXiv:2502.09433 (com D. de Almeida) PDF

Artigos Publicados

  1. Rigidity of min–max minimal disks in 3-balls with non-negative Ricci curvature. Calc. Var. Partial Differ. Equ. 64 (2025), No. 4, Paper No. 133, 32 p. doi.org/10.1007/s00526-025-02984-w (com L. Mazet) PDF
  2. Some rigidity results for charged initial data sets. Nonlinear Anal. 256 (2025), Article ID 113780, 9 p. doi.org/10.1016/j.na.2025.113780 (com G.J. Galloway) PDF
  3. Aspects of the geometry and topology of expanding horizons. Proc. Am. Math. Soc. 153 (2025), No. 3, 1239-1250. doi.org/10.1090/proc/17092 (com G.J. Galloway)
  4. Some rigidity results for compact initial data sets. Trans. Am. Math. Soc. 377 (2024), No. 3, 1989-2007. doi.org/10.1090/tran/9079 (com G.J. Galloway) PDF
  5. Free boundary minimal hypersurfaces outside of the ball. Rev. Mat. Iberoam. 40 (2024), No. 1, 277-298. doi.org/10.4171/rmi/1453 (com L. Mazet) PDF
  6. Rigidity of free boundary MOTS. Nonlinear Anal. 220 (2022), Article ID 112841, 15 p. doi.org/10.1016/j.na.2022.112841 PDF
  7. Initial data rigidity results. Commun. Math. Phys. 386 (2021), No. 1, 253-268. doi.org/10.1007/s00220-021-04033-x (com M. Eichmair e G.J. Galloway) PDF
  8. Rigidity of marginally outer trapped (hyper)surfaces with negative σ-constant. Trans. Am. Math. Soc. 372 (2019), No. 8, 5851-5868. doi.org/10.1090/tran/7752 PDF
  9. Rigidity of volume-minimising hypersurfaces in Riemannian 5-manifolds. Math. Proc. Camb. Philos. Soc. 167 (2019), No. 2, 345-353. doi.org/10.1017/S0305004118000361 PDF
  10. Characterization of hypersurfaces via the second eigenvalue of the Jacobi operator. Proc. Am. Math. Soc. 147 (2019), No. 8, 3515-3521. doi.org/10.1090/proc/14477 PDF
  11. Vanishing theorems for the cohomology groups of free boundary submanifolds. Ann. Global Anal. Geom. 56 (2019), No. 1, 137-146. doi.org/10.1007/s10455-019-09660-1 (com M.P. Cavalcante e F. Vitório) PDF
  12. Rigidity of free boundary surfaces in compact 3-manifolds with strictly convex boundary. J. Geom. Anal. 28 (2018), No. 2, 1245-1257. doi.org/10.1007/s12220-017-9861-9 PDF
  13. Rigidity of marginally outer trapped 2-spheres. Commun. Anal. Geom. 26 (2018), No. 1, 63-83. doi.org/10.4310/CAG.2018.v26.n1.a2 (com G.J. Galloway) PDF