Alexandre Fernandes's Webpage

Published Papers

(with F. Fernandes, E. Sampaio and J. Silva) Bi-Hölder equivalence of real analytic functions. Research in Mathematical Sciences Volume 11, Article number 20 (2024). DOI: 10.1007/s40687-024-00429-y.
(with E. Sampaio) On characterization of smoothness of complex analytic sets. Indiana Univrsity Mathetatics Journal 72 No 6 (2023), 2547-2565. DOI: 10.1512/iumj.2023.72.9657.
(with Z. Jelonek) Bi-Lipschitz Characterization of Space Curves. Bulletin of the Brazilian Mathematical Society, New Series, Article number 29 (2023). DOI: 10.1007/s00574-023-00348-6
(with E. Sampaio) Global bi-Lipschitz classification of semialgebraic surfaces. Accepted for publication in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (2022), 21 pages. DOI: 10.2422/2036-2145.202206_005
(with Z. Jeonek and E. Sampaio) On the Fukui–Kurdyka–Paunescu conjecture. Compositio Mathematica 158 (2022), 1298--1313. DOI:10.1112/S00010437X22007631
(with L. Birbrair and Z. Jelonek) On the extension of bi-Lipschitz mappings. Selecta Math New Series 27 (2021) 15 pages. DOI: 10.1007/s00029-021-00625-6

(with L. Birbrair, E. Sampaio and M. Verbitsky) Multiplicity of singularities is not a bi-Lipschitz invariant. Mathematische Annalen 377 (2020), 115--121. DOI:10.1007/s00208-020-01958-x

(with V. Grandjean and C.H Soares Jr) A note on the local Lipschitz triviality of values of complex polynomial functions. Mathematische Zeitschrift. 296, 861–874 (2020). DOI:10.1007/s00209-020-02474-z

(with J. Edson Sampaio) On Lipschitz rigidity of complex analytic sets. The Journal of Geometric Analysis. Volume 30, Issue 1, January 2020, 706-718. DOI:10.1007/s12220-019-00162-x

(with E. Sampaio) Tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded. Appendix by Anne Pichon and Walter D. Neumann. International Mathematics Research Notices. Volume 2019, Issue 15, August 2019, Pages 4880–4897. DOI: 10.1093/imrn/rnx290/4782490

(with J. Fernández de Bobadilla and E. Sampaio) Multiplicity and degree as bi-Lipschitz invariants for complex sets. Journal of Topology 11, issue 4 (2018), 957-965. DOI: 10.1112/topo.12080

(with J. Edson Sampaio and Joserlan P. Silva) Hölder equivalence of complex analytic curve singularities. Bulletin of the London Mathematical Society 50, issue 5 (2018), 874-886. DOI: 10.1112/blms.12192

(with L. Birbrair, T. Gaffney, and V. Grandjean). Blow-Analytic equivalence versus K-bi-Lipschitz Equivalence. Journal of the Mathematical Society of Japan 70, No 3 (2018), 989-1006. DOI: 10.2969/jmsj/74237423

(with L. Birbrair and V. Grandjean). Thin-thick decomposition for real definable isolated singularities. Indiana Univ. Math. J. 66, No 2, (2017), 547--557. DOI: 10.1512/iumj.2017.66.6008

(with L. Birbrair, A. Gabrielov and V. Grandjean). Lipschitz contact equivalence of function germs in R2. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XVII (2017), 81--92. DOI: 10.2422/2036-2145.201503_014

(with J. Edson Sampaio). Multiplicity of analytic hypersurface singularities under bi-Lipschitz homeomorphisms Journal of Topology 9 (2016), pp 927--933. DOI: 10.1112/jtopol/jtw014

(with L. Birbrair, J. Edson Sampaio, Le D. T.) Lipschitz regular complex algebraic sets are smooth Proc. Amer. Math. Soc. 144 (2016), pp 983--987. DOI: 10.1090/proc/12783

(with L. Birbrair, V. Grandjean) On the bi-Lipschitz contact equivalence of plane complex function- germs Journal of Singularities 13 (2015), pp 01-10. DOI: 10.5427/jsing.2015.13a

(with J. L. M. Barbosa, L. Birbrair and M. P. do Carmo). Globally subanalytic CMC surfaces in R3 Electronic Research Announcements in Math. Sci. 21 (2014), pp 186-192. DOI: 10.3934/era.2014.21.186

(with C. Maquera and J. Venato Santos) Jacobian Conjecture and semi-algebraic maps. Math. Proc. of the Cambridge Philos. Soc. 157 (2014), pp 221-229. DOI: 10.1017/S0305004114000279

(with L. Birbrair, V. Grandjean and D. O'Shea) Choking horns in Lipschitz geometry of complex algebraic varieties. Appendix by W. D. Neumann.J. Geom. Anal. 24 (2014), pp 1971-1981, DOI: 10.1007/s12220-013-9405-x

(with M. Ruas) Rigidity of bi-Lipschitz equivalence of weighted homogeneous function-germs in the plane.Proc. Amer. Math. Soc. 141 (2013), 1125--1133. DOI: 10.1090/S0002-9939-2012-11388-7

Fast loops on semi-weighted homogeneous hypersurface singularities. Journal of Singularities 1 (2010), 85--93. DOI: 10.5427/jsing.2010.1f

(with L. Birbrair and W. D. Neumann) Separating sets, metric tangent cone and applications for complex algebraic germs. Selecta Math. (NS) 16 (2010), 377--491. DOI: 10.1007/s00029-010-0024-0

(with L. Birbrair and W. D. Neumann) Normal embedding of complex algebraic surfaces. Real and Complex Singularities. LMS Lecture Note Series 380 (2010).
(with S. Alvarez, L. Birbrair and J. C. F. Costa) Topological k-equivalence of analytic function-germs. Central European Journal of Mathematics 8 (2010), n. 2, 338--345. DOI: 10.2478/s11533-010-0013-8

(with L. Birbrair, J. C. F. Costa) Topological contact equivalence of map germs. Hokkaido Mathematical Journal 38 (2009), n. 3, 511-517.
(with L. Birbrair and W. D. Neumann) Bi-Lipschitz geometry of complex surface singularities. Geom. Dedicata 139 (2009), n. 1, 259--267. DOI: 10.1007/s10711-008-9333-2

(with L. Birbrair and D. Panazzolo) Lipschitz classification of functions on Holder triangle. St. Petersburg Math. J. 20 (2009), 681--686. DOI: 10.1090/S1061-0022-09-01067-X

Original publication in Algebra i Analiz 20 (2008),n. 5, 1--9.

(with L. Birbrair) Local metric properties of semi-quasihomogeneous real surfaces. Topology and its Applications 155 (2008),n. 16,1772--1776. DOI: 10.1016/j.topol.2008.05.023

(with L. Birbrair and W. D. Neumann) Bi-Lipschitz geometry of weighted homogeneous surface singularities. Math. Ann. 342 (2008), n. 1, 139--144. DOI: 10.1007/s00208-008-0225-4

(with L. Birbrair) Local Lipschitz geometry of real weighted homogeneous surfaces. Geom. Dedicata 135 (2008),n. 1, 211--217. DOI: 10.1007/s10711-008-9271-z

(with L. Birbrair) Inner metric geometry of complex algebraic surfaces with isolated singularities. Comm. Pure Appl. Math. 61 (2008), n. 11, 1483--1494. DOI: 10.1002/cpa.20244

(with L. Birbrair, J. C. F. Costa and M. Ruas ) K-bi-Lipschitz equivalence of real function-germs. . Amer. Math. Soc. 135 (2007), n. 4, 1089--1095. DOI: 10.1090/S0002-9939-06-08566-2

(with R. dos Santos and Soares Junior) Topological triviality of family of functions and sets. Rocky Mountain J. Math. 36 (2006), n. 4, 1235--1247. DOI: 10.1216/rmjm/11810694142

(with C. Gutierrez and R. Rabanal) Global asymptotic stability for differentiable vector fields of R2. J. Differential Equations 206 (2004), n. 2, 470--482. DOI: 10.1016/j.jde.2004.04.015

(with Soares Junior) On the bilipschitz triviality of families of real maps. Real and complex singularities, 95--103, Contemp. Math. 354 , Amer. Math. Soc., Providence, RI, 2004.
(with M. Ruas) Bi-Lipschitz determinacy of quasihomogeneous germs. Glasg. Math. J. 46 (2004), n. 1, 77--82. DOI: 10.1017/S001708950300154X

(with C. Gutierrez and R. Rabanal) On local diffeomorphisms of Rn that are injective.Qual. Theory Dyn. Syst. 4 (2004), n. 2, 255--262. DOI: 10.1007/BF02970861

(with L. Birbrair) Metric theory of semialgebraic curves. Rev. Mat. Complut. 13 (2000), n. 2, 369--382. DOI: 10.5209/rev_REMA.2000.v13.n2.17080