Published and accepted
(with L. Birbrair, A. Fernandes and Lê D. T.) Lipschitz regular complex algebraic sets are smooth. Proc. Amer. Math. Soc., vol. 144 (2016), 983-987. [DOI] [Arxiv] [PDF]
Bi-Lipschitz homeomorphic subanalytic sets have bi-Lipschitz homeomorphic tangent cones. Selecta Mathematica: New Series, vol. 22 (2016), no. 2, 553-559. [DOI] [Arxiv] [PDF]
(with A. Fernandes) Multiplicity of analytic hypersurface singularities under bi-Lipschitz homeomorphisms. Journal of Topology, vol. 9 (2016), 927-933. [DOI] [Arxiv] [PDF]
(with A. Fernandes and J. P. Silva) H\"older equivalence of complex analytic curve singularities. Bull. London Math. Soc., vol. 50 (2018), no. 5, 874-886. [DOI] [Arxiv] [PDF]
(with A. Fernandes and J. Fernández-Bobadilla) Multiplicity and degree as bi-Lipschitz invariants for complex sets. Journal of Topology, vol. 11 (2018), no. 4, 957-965. [DOI] [Arxiv] [PDF]
On Zariski's multiplicity problem at infinity. Proc. Amer. Math. Soc., vol. 147 (2019), 1367-1376. [DOI] [Arxiv] [PDF]
A proof of the differentiable invariance of the multiplicity using spherical blowing-up. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, vol. 113 (2019), no. 4, 3913-3920. [DOI] [PDF]
(with A. Fernandes) Tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded. Appendix by Anne Pichon and Walter D. Neumann. International Mathematics Research Notices, vol. 2019 (2019), no. 15, 4880-4897. [DOI] [Arxiv] [PDF]
(with A. Fernandes) On Lipschitz rigidity of complex analytic sets. The Journal of Geometric Analysis, vol. 30 (2020), 706-718. [DOI] [Arxiv] [PDF]
(with L. Birbrair, A. Fernandes and M. Verbitsky) Multiplicity of singularities is not a bi-Lipschitz invariant. Mathematische Annalen, vol. 377 (2020), 115-121. [DOI] [Arxiv] [PDF]
Multiplicity, regularity and blow-spherical equivalence of complex analytic set. The Asian Journal of Mathematics, vol. 24 (2020), no. 5, 803-820. [DOI] [Arxiv] [PDF]
Globally subanalytic CMC surfaces in $\mathbb{R}^3$ with singularities. Proceedings A of the Royal Society of Edinburgh, vol. 151 (2021), no. 1, 407-424. [DOI] [RG] [PDF]
Multiplicity, regularity and Lipschitz Geometry of real analytic hypersurfaces. Israel Journal of Mathematics, vol. 246 (2021), no. 1, 371–394. [DOI] [RG] [PDF]
Differential invariance of the multiplicity of real and complex analytic sets. Publicacions Matemàtiques, vol. 66 (2022), 355–368. [DOI] [Arxiv] [RG] [PDF]
(with J. Fernández-Bobadilla and G. Peñafort-Sanchis). Topological invariants and Milnor fibre for A-finite germs C 2 → C 3. Dalat University Journal of Science, vol. 12 (2022), no. 2, 19-25. [DOI] [Arxiv] [RG] [PDF]
Multiplicity, regularity and blow-spherical equivalence of real analytic sets. Mathematische Zeitschrift, vol. 301 (2022), 385–410. [DOI] [RG] [PDF]
(with A. Fernandes and Z. Jelonek) On the Fukui-Kurdyka-Paunescu Conjecture. Compositio Mathematica, vol. 158 (2022), no. 6, 1298-1313. [DOI] [arXiv] [RG] [PDF]
(with J. Fernández-Bobadilla, S. Heinze and M. Pe-Pereira) Moderately Discontinuous Homology. Communications on Pure and Applied Mathematics, vol. 75 (2022), no. 10, 2123-2200. [DOI] [Arxiv] [RG] [PDF] [Awarded Prêmio SBM, 2025]
(with E. C. da Silva) On bi-Lipschitz invariance and the uniqueness of tangent cones. Journal of Singularities, vol. 25 (2022), 393-402. [DOI] [RG] [PDF]
On Lipschitz Geometry at infinity of complex analytic sets. Calculus of Variations and Partial Differential Equations, vol. 62 (2023), no. 2, article number 69. [DOI] [arXiv] [RG] [PDF]
(with A. Fernandes) On characterization of smoothness of complex analytic sets. Indiana University Mathematics Journal, vol. 72 (2023), no. 6, 2547-2565. [DOI] [arXiv] [RG] [PDF]
(with E. C. da Silva) Classification of real algebraic curves under blow-spherical homeomorphisms at infinity. São Paulo Journal of Mathematical Sciences, vol.18 (2024), 1269–1283. [DOI] [arXiv] [RG] [PDF]
(with A. Fernandes, F. Fernandes and J. P. Silva) Bi-H\"older equivalence of real analytic functions. Research in the Mathematical Sciences, vol. 11 (2024), article 20, 1-6. [DOI] [arXiv] [RG] [PDF]
(with R. Mendes) On the link of Lipschitz normally embedded sets. International Mathematics Research Notices IMRN, vol. 2024 (2024), no. 9, 7488-7501. [DOI] [arXiv] [RG] [PDF]
(with A. Fernandes) Global bi-Lipschitz classification of semialgebraic surfaces. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, vol. XXV (2024), 1505-1526. [DOI] [arXiv] [RG] [PDF]
Local versus global Lipschitz geometry. Journal of the London Mathematical Society, vol. 110 (2024), no. 5, e70011, 20 pp. [DOI] [arXiv] [RG] [PDF]
(with E. C. da Silva) Classification of complex algebraic curves under blow-spherical equivalence. Revista Matemática Complutense, vol. 38 (2025), 419–443. [DOI] [arXiv] [RG] [PDF]
(with L. Bibrair, M. Denkowski and D. L. Medeiros) Universality theorem for LNE Hölder triangles. International Mathematics Research Notices IMRN, vol. 2025 (2025), no. 11, rnaf123, 1-9. [DOI] [arXiv] [RG] [PDF]
(with D. L. Medeiros and E. Souza) Moderately discontinuous homology of real surfaces. Selecta Mathematica: New Series, vol. 31 (2025), article no. 82, 37 pp. [DOI] [arXiv] [RG] [PDF]
Log-Lipschitz regularity and Hölder regularity imply smoothness for complex analytic sets. Journal of the European Mathematical Society, vol. online (2025), 23pp. [DOI] [arXiv] [RG] [PDF]
Pre-prints
(with A. Fernandes and Z. Jelonek) Bi-Lipschitz equivalent cones with different degrees. Submitted for publication (2023). [arXiv] [RG] [PDF]
(with A. Fernandes and J. P. Silva) H\"older invariance of the Henry-Parusinski invariant. Submitted for publication (2024). [arXiv] [RG] [PDF]
(with A. Fernandes and Z. Jelonek) On metric equivalence of the Brieskorn-Pham hypersurfaces. Submitted for publication (2024). [arXiv] [RG] [PDF]
(with E. C. da Silva) Bounds to the mean curvature of leaves of CMC foliations. Submitted for publication (2024). [arXiv] [RG] [PDF]
(with L. Câmara and F. Reis) On the topological invariance of the algebraic multiplicity of holomorphic foliations. Submitted for publication (2024). [arXiv] [RG] [PDF]
(with E. C. da Silva) On the Kurdyka-Raby Formula at infinity and the Moser's Bernstein Theorem. Submitted for publication (2024). [arXiv] [RG] [PDF]
Real and bi-Lipschitz versions of the Theorem of Nobile. Submitted for publication (2025). [arXiv] [RG] [PDF]
On the Milnor fibres of initial forms of topologically equivalent holomorphic functions. Submitted for publication (2025). [arXiv] [RG] [PDF]
(with R. de Omena and E. Souza) On the Invariance of the Real Milnor Number under Asymptotically Lipschitz Equivalence. Submitted for publication (2025). [arXiv] [RG] [PDF]
(with E. C. da Silva) Bounds to the mean curvature of leaves of CMC good foliations. Submitted for publication (2025). [arXiv] [RG] [PDF]
(with A. Gadelha Rocha) Lipschitz regularity of definable sets. (2025). [arXiv] [RG] [PDF]
(with J. J. Nuño Ballesteros, V. de Oliveira Prado, G. Peñafort Sanchis) Lipschitz geometry of the image of finite mappings. (2025). [arXiv] [RG] [PDF]
(with D. L. Medeiros and E. L. Sanchez Quiceno) Lipschitz Geometry of Mixed Polynomials. Submitted for publication (2025). [arXiv] [RG] [PDF]
(with A. Fernandes and Z. Jelonek) Proof of the metric Arnold's corank problem. Submitted for publication (2025). [arXiv] [RG] [PDF]
Chapters
Some homeomorphisms that preserve tangent cones and multiplicity. Contemporary Mathematics, vol. 742 (2020), 189-200. [DOI] [Arxiv] [PDF]
(with A. Fernandes) Bi-Lipschitz Invariance of the Multiplicity. In: Cisneros-Molina, J.L., Dũng Tráng, L., Seade, J. (eds) Handbook of Geometry and Topology of Singularities IV. Springer, Cham (2023). [DOI] [arXiv] [RG] [PDF]
Books
(with A. Fernandes) Lipschitz geometry of complex singularities. Coleção Colóquios Brasileiros de Matemática. IMPA, Rio de Janeiro (July 2025).