Rafael Montezuma

CV Lattes (in Portuguese)        Teaching

Professor of Mathematics at the Department of Mathematics - UFC (Fortaleza, CE, Brazil).

Contact Information: montezuma [at] mat.ufc.br

Papers

• The min-max width of spheres associated to the distance function. (submitted) (with Idalina Ribeiro) arXiv

• The width of embedded circles. (Crelles Journal), vol. 2025, no. 824, 2025, pp. 289-332. (with Lucas Ambrozio and Roney Santos) DOI arXiv

• The first width of non-negatively curved surfaces with convex boundary. J. Geom. Anal. 34 (2024), no. 2, 60. (with Sidney Donato) DOI arXiv

• Morse inequalities for the area functional. J. Differential Geom. 124 (2023), no. 1, 81–111. (with Fernando Codá Marques and André Neves) DOI arXiv

• On free-boundary minimal surfaces in the Riemannian Schwarzschild manifold. Bull. Braz. Math. Soc. (N.S.) 52 (2021), no. 4, 1055–1071. DOI arXiv

• On the min-max width of unit volume three-spheres. J. Differential Geom. 126(3): 875-907. (with Lucas Ambrozio)  DOI arXiv

• On the two-systole of real projective spaces. Rev. Mat. Iberoam. 36 (2020), no. 7, 1979–1988. (with Lucas Ambrozio) DOI arXiv

• A mountain pass theorem for minimal hypersurfaces with fixed boundary. Calc. Var. Partial Differential Equations 59 (2020), no. 6, Paper No. 188, 30 pp. DOI arXiv 

• Metrics of positive scalar curvature and unbounded min-max widths. Calc. Var. Partial Differential Equations 55 (2016), no. 6, Art. 139, 15 pp. DOI arXiv 

• Min-max minimal hypersurfaces in non-compact manifolds. J. Differential Geom. 103 (2016), no. 3, 475–519. DOI arXiv 

Books

• Métodos Min-max em Geometria: uma introdução (in Portuguese) (with Lucas Ambrozio). Editora do IMPA (2025). CBM 2025

PhD students

• Thiago Lima Gonçalves (PhD, 2029 expected)

• Idalina Maria Ribeiro Silva (PhD, 2026 expected)

Masters students

• Sayd de Moura Luz (MSc, 2027 expected) 

• Carlos Ferreira Argemiro Filho (MSc, 2026 expected)

• Joel Vitor Barreto Santos (MSc, 2025)

• Renan Braz Parente (MSc, 2023)

• Paulo Henryque da Costa Silva (MSc, 2022)

Undergraduate Students 

• Igor Pinheiro Freire Ximenes (PIBIC-UFC Fellowship, 2023-current)

• Carlos Daniel Dutra do Monte (UFC, Serrapilheira Fellowship, 2024-current)

• Sayd de Moura Luz (UFPI, Serrapilheira Fellowship, 2023-2024)

• Samuel Cantoaria Ferreira (UFMA, Serrapilheira Fellowship, 2023-2024)

• Francisco Donato Leite Pessoa (PIBIC-UFC CNPq Fellowship, 2022-2024)

• Maria Eduarda Bezerra de Oliveira (PIBIC-UFC CNPq and Serrapilheira Fellowships, B. Math. 2021-2022)

• Camilly Maria Ferreira Cordeiro (PIBIC-UFC, CNPq Fellowship, 2022-2023)

Postdocs: Roney Santos (2022-2023), Julieth Saavedra (2022-2024), Luciano Luzzi Junior (2024)

Grants and awards

• Research Grant CNPq-level B (2025-2029)

• Instituto Serrapilheira Grant, 2021-2026.

• Chebyshev Grant, ICM 2022.

• Research Grant CNPq-level 2 (2021-2024)

• Carlos Gutierrez PhD Thesis Prize, ICMC - USP São Carlos  (2016).

• CAPES PhD Thesis Prize in Mathematics (2016). 

• IV Prêmio de Iniciação Científica (Jornadas de Iniciação Cientifica - IMPA - 2008).