Publications

Survey:

On subanalytic geometry

Published articles:

• On the Laplace equation on bounded subanalytic manifolds, Calculus of Variations and Partial Differential Equations vol. 63, (2024) article no. 236
• Trace operators on bounded subanalytic manifolds (with Anna Valette), Selecta Mathematica vol. 30, 54 (2024)
• On Sobolev spaces of bounded subanalytic manifolds, Mathematische Annalen vol. 390 (2024), 2413–2457
• Regular Vectors and Bi-Lipschitz Trivial Stratifications in O-Minimal Structures, in "Handbook of Geometry and Topology of Singularities IV", Springer (2023) (arXiv)
• A remark on C^∞ definable equivalence (with Anna Valette), Annales Polonici Mathematici vol. 131.1 (2023), 79-84
• Uniform Poincare inequality in o-minimal structures (with Anna Valette), Mathematical Inequalities and Applications vol. 26 (2023), 141-150 
• Approximations in globally subanalytic and Denjoy-Carleman classes (with Anna Valette), Advances in Mathematics vol. 385 (2021), 107764 
• Poincaré Inequality on Subanalytic Sets (with Anna Valette), Journal of Geometric Analysis vol. 31 (2021), 10464–10472
• Poincaré duality for L^p cohomology on subanalytic singular spaces, Mathematische Annalen vol. 380 (2021), 789–823
• Whitney stratifications and the continuity of local Lipschitz Killing curvatures (with Nhan Nguyen), Annales de l'Institut Fourier vol. 68 no.5 (2018), 2253-2276
• On the local geometry of definably stratified sets (with David Trotman), in Contemporary Mathematics (2017), "Ordered algebraic structures and related topics", American Mathematical Society (AMS) (arXiv)
• A generalized Sard theorem on real closed fields (with Anna Valette), Mathematische Nachrichten vol. 289 , no 5-6 (2016), 748–755
• Lipschitz stratifications in o-minimal structures (with Nhan Nguyen), Annales Scientifiques de l'Ecole Normale Superieure vol. 49 (no.2) (2016), 399–421
• Stokes' formula for stratified forms, Annales Polonici Mathematici vol. 114 (2015), 197-206
• Arc-quasianalytic functions (with Edward Bierstone and Pierre Milman), Proceedings of the American Mathematical Society vol. 143 (2015), 3915-3925
• On the geometry of polynomial mappings at infinity (with Anna Valette), Annales de l'Institut Fourier vol. 64, fascicule 5 (2014), 2147-2163
• A Lefschetz duality for intersection homology, Geometriae Dedicata vol. 169, issue 1 (2014), 283-299
• On a singular variety associated to a polynomial mapping (with Nguyen Thi Bich Thuy and Anna Valette), Journal of Singularities vol. 7 (2013), 190-204
• Vector bundles and regulous maps (with Marcin Bilski, Wojciech Kucharz and Anna Valette), Mathematische Zeitschrift vol. 275, no. 1-2 (2013), 403–418
• On bi-Lipschitz stability of families of functions, Journal of Singularities vol. 6 (2012), 179-198
• L^∞ cohomology is intersection cohomology, Advances in Mathematics vol. 231 (2012), 1818-1842
• C⁰ and bi-Lipschitz K-equivalence (with Maria Ruas), Mathematische Zeitschrift vol. 269 (2011), 293-308
• De Rham theorem for L^∞ forms and homology on singular spaces (with Leonid Sharster), C. R. Math. Acad. Sci. Soc. R. Can vol. 32 (2010)
• Vanishing homology, Selecta Mathematica-New Series vol. 16 (2010), 267-296
• Multiplicity mod 2 as a metric invariant, Discrete and Computational Geometry vol. 43 (2010), 663-679
• Notes on vanishing homology, C. R. Math. Acad. Sci. Soc. R. Can vol. 31 (2009), 118-126
• Bi-Lipschitz trivial quasi-homogeneous stratifications (with Dwi Juniati), Saitama Mathematical Journal vol. 26 (2009), 1-13
• Bi-Lipschitz sufficiency of jets, Journal of Geometric Analysis vol. 19 (2009), 963-993
• On metric types that are definable in an o-minimal structure, Journal of Symbolic Logic vol. 73 (2008), 439-447
• Volume, Whitney conditions and Lelong number, Annales Polonici Mathematici vol. 93 (2008), 1-16
• The link of the germ of a semi-algebraic metric space, Proceedings of the American Mathematical Society vol. 135 (2007), 3083-3090
• Lipschitz triangulations, Illinois Journal of Mathematics vol. 49 (2005), 953-979
• Volume and multiplicities of real analytic sets, Annales Polonici Mathematici vol. 87 (2005), 265-276
• A bilipschitz version of Hardt's theorem, Comptes Rendus Mathematique vol. 340 (2005), 895-900
• Lipschitz stratifications and generic wings (with Dwi Juniati and David Trotman), Journal of the London Mathematical Society vol. 68 (2003), 133-147

Preprints on arXiv.org:

• L^p Hodge theory for bounded subanalytic manifolds