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This independent catalogue makes OpenAI’s collection of 722 mathematics preprints easier to explore. Papers are organized by research area, with clickable keywords, full-text search covering proofs and references, and direct links to the original manuscripts. Each entry also identifies the documented status and scope of Lean formalization. The catalogue reflects the repository as of October 7, 2026.
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2026 and later
[92] P. Hajłasz, A. Schikorra, Hölder embeddings of a disk into the Heisenberg group H^1 (Preliminary manuscript prepared with GPT-6 Astra). [Link].
This is an AI-assisted preliminary manuscript. The proposed proof and its calculations have not yet been verified by the human authors. We will keep updating the manuscripts.
[91] B. Esmayli, P. Goldstein, P. Hajłasz, Differentiability of Lipschitz mappings into metric spaces: area and co-area formulas. [arXiv]
[90] R. Alvarado, A. Dughayshim, P. Hajłasz, The Trudinger inequality is true for $M^{1,s}$ spaces. [arXiv]
[89] P. Hajłasz, J. Mirra, A. Schikorra, Hölder continuous mappings, differential forms and the Heisenberg groups. [arXiv]
[88] P. Hajłasz, A. Schikorra, On the Gromov non-embedding theorem. Proc. Amer. Math. Soc. 154 (2026), 3973–3981. [arXiv]
[87] P. Goldstein, P. Hajłasz, $C^2$-Lusin approximation of convex functions: one variable case. J. Math. Anal. Appl. 557 (2026), no. 2, Paper No. 130333 [arXiv]
2025
[86] P. Goldstein, Z. Grochulska, P. Hajłasz, Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms. Expositiones Math. 43 (2025) 125681 [arXiv]
[85] D. Azagra, M. Drake, P. Hajłasz, $C^2$-Lusin approximation of strongly convex bodies. J. Convex Anal. 32 (2025), 91-106. [arXiv]
[84] P. Goldstein, Z. Grochulska, P. Hajłasz, Constructing diffeomorphisms and homeomorphisms with prescribed derivative. Adv. Math. 460 (2025) 110020, 65 pp. [arXiv]
2024 and later
[83] D. Azagra, M. Drake, P. Hajłasz, $C^2$-Lusin approximation of strongly convex functions. Inventiones Math. 236 (2024), 1055-1082. (free online access) [arXiv]
2023
[82] D. Azagra, A. Cappello, P. Hajłasz, A geometric approach to second-order differentiability of convex functions. Proc. Amer. Math. Soc. Ser. B 10 (2023), 382-397. [arXiv]
[81] R. Alvarado, P. Hajłasz, L. Maly, A simple proof of reflexivity and separability of $N^{1,p}$ Sobolev spaces. Annales Fennici Mathematici 48 (2023), 255–275. [arXiv]
[80] P. Goldstein, P. Hajłasz Smooth approximation of mappings with rank of the derivative at most 1. Calc. Var. Partial Differential Equations 62 (2023), no. 3, Paper No. 88. [arXiv]
2020
[75] P. Goldstein, P. Hajłasz, P. Pankka, Topologically nontrivial counterexamples to Sard's theorem Int. Mat. Res. Not. IMRN 2020, no. 20, 7073-7096. [arXiv]
[74] P. Hajłasz, S. Zimmerman, An implicit function theorem for Lipschitz mappings into metric spaces. Indiana Univ. Math. J. 69 (2020), 205–228. [arXiv]
[73] R. Alvarado, P. Gorka, P. Hajłasz, Sobolev embedding for $M^{1,p}$ spaces is equivalent to a lower bound of the measure. J. Funct. Anal. 279 (2020), no. 7 108628, 39 pp. [arXiv]
[72] R. Alvarado, P. Hajłasz, A note on metric-measure spaces supporting Poincare inequalities Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 31 (2020), 15-23. [arXiv]
[71] M. Bonk, L. Capogna, P. Hajłasz, N. Shanmugalingam, J. T. Tyson, Analysis on metric spaces, Notices AMS. 67 (2020), 253-256. [arXiv]
2019
[70] P. Hajłasz, Linking topological spheres. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), 907-909. [arXiv]
[69] P. Goldstein, P. Hajłasz, Jacobians of $W^{1,p}$ homeomorphisms, case $p=[n/2]$. Calc. Var. Partial Differential Equations 58 (2019), no. 4, Paper No. 122, 28 pp. [arXiv]
[68] P. Goldstein, P. Hajłasz, M. R. Pakzad, Finite distortion Sobolev mappings between manifolds are continuous. Int. Math. Res. Not. IMRN. 2019, no. 14, 4370–4391. [arXiv]
[67] P. Goldstein, P. Hajłasz, Topological obstructions to continuity of Orlicz-Sobolev mappings of finite distortion. Ann. Mat. Pura Appl. 198 (2019), 243-262. [arXiv]
2018
[66] P. Hajłasz, S. Malekzadeh, S. Zimmerman, Weak BLD mappings and Hausdorff measure. Nonlinear Analysis. 177 (2018), 524-531. [arXiv]
[65] P. Goldstein, P. Hajłasz, $C^1$ mappings in $R^5$ with derivative of rank at most 3 cannot be uniformly approximated by $C^2$ mappings with derivative of rank at most 3 J. Math. Anal. Appl. 468 (2018), 1108-1114. [arXiv]
[64] P. Goldstein, P. Hajłasz, Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian. Ann. Acad. Sci. Fenn. Math. 43 (2018), 147-170. [arXiv]
[63] P. Hajłasz, The (n+1)-Lipschitz homotopy group of the Heisenberg group Hn. Proc. Amer. Math. Soc. 146 (2018), 1305-1308. [arXiv]
2017
[62] P. Hajłasz, S. Zimmerman, Dubovitskij-Sard theorem for Sobolev mappings. Indiana Univ. Math. J. 66 (2017), 705-723. [arXiv]
[61] P. Goldstein, P. Hajłasz, A measure and orientation preserving homeomorphism of a cube with Jacobian equal $-1$ almost everywhere. Arch. Ration. Mech. Anal. 225 (2017), 65-88. [arXiv]
[60] P. Hajłasz, Z. Liu, A Marcinkiewicz integral type characterization of the Sobolev space. Publ. Mat. 61 (2017), 83-104. [arXiv]
[59] P. Hajłasz, M. V. Korobkov, J. Kristensen. A bridge between Dubovitskii-Federer theorems and the coarea formula J. Funct. Anal. 272 (2017), 1265-1295. [arXiv]
2016
[58] P. Hajłasz, X. Zhou, Sobolev homeomorphism on a sphere containing an arbitrary Cantor set in the image. Geom. Dedicata 184 (2016), 159-173. [arXiv]
2015
[57] P. Hajłasz, S. Malekzadeh, A new characterization of the mappings of bounded length distortion. Int. Math. Res. Not. IMRN 2015, no. 24, 13238-13244. [arXiv]
[56] P. Hajłasz, S. Zimmerman, Geodesics in the Heisenberg group. Anal. Geom. Metr. Spaces 3 (2015), 325-337. [arXiv]
[55] P. Hajłasz, S. Malekzadeh, On conditions for unrectifiability of a metric space. Anal. Geom. Metr. Spaces 3 (2015), 1-14. [arXiv]
2014
[54] Z. M. Balogh, P. Hajłasz, K. Wildrick, Weak contact equations for mappings into Heisenberg groups. Indiana Univ. Math. J. 63 (2014), 1839-1873. [arXiv]
[53] P. Hajłasz, Z. Liu, Maximal potentials, maximal singular integrals and the spherical maximal function. Proc. Amer. Math. Soc. 142 (2014), 3965-3974. [arXiv]
[52] P. Hajłasz, A. Schikorra, Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 39 (2014), 593-604. [arXiv]
[51] N. DeJarnette, P. Hajłasz, A. Lukyanenko, J. Tyson, On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target. Conform. Geom. Dyn. 18 (2014), 119-156. [arXiv]
[50] P. Hajłasz, A. Schikorra, J. Tyson, Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups Geom. Funct. Anal.24 (2014), 245-268. [arXiv]
2013
[49] P. Hajłasz, Z. Liu, Sobolev spaces, Lebesgue points and maximal functions J. Fixed Point Theory Appl. 13 (2013), 259-269. [arXiv]
[48] P. Hajłasz, J. Mirra, The Lusin theorem and horizontal graphs in the Heisenberg group Anal. Geom. Metr. Spaces 1 (2013), 295-301. [pdf]
[47] J. Gong, P. Hajłasz, Differentiability of p-harmonic functions on metric measure spaces. Potential Analysis 38 (2013), 79-93. [pdf]
2012
[46] P. Goldstein, P. Hajłasz, Sobolev mappings, degree, homotopy classes and rational homology spheres. J. Geom. Anal. 22 (2012), 320-338. [pdf]
2011
[45] P. Hajłasz, Sobolev mappings: Lipschitz density is not an isometric invariant of the target. Int. Math. Res. Not. IMRN Vol. 2011, no.12, 2794-2809. [pdf]
2010
[44] P. Hajłasz, Z. Liu, A compact emebdding of a Sobolev space is equivalent to an emebdding into a better space. Proc. Amer. Math. Soc.138 (2010), 3257-3266. [pdf]
[43] P. Hajłasz, J. Maly, On approximate differentiability of the maximal function. Proc. Amer. Math. Society. 138 (2010), 165--174. [pdf]
2009
[42] P. Hajłasz, Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces. Math. Ann. 343 (2009), 801-823. [pdf]
[41] P. Hajłasz, Sobolev mappings between manifolds and metric spaces. In: Sobolev Spaces in Mathematics I. Sobolev type Inequalities pp. 185-222. International Mathematical Series. Springer 2009. [pdf]
2008
[40] P. Hajłasz, J. Tyson, Sobolev Peano cubes. Michigan Math. J. 56 (2008), 687-702. [pdf]
[39] P. Hajłasz, P. Strzelecki, X. Zhong, A new approach to interior regularity of elliptic systems with quadratic Jacobain structure in dimention two. Manuscripta Math. 127 (2008), 121-135. [pdf]
[38] P. Hajłasz, P. Koskela, H. Tuominen, Measure density and extendability of Sobolev functions Rev. Mat. Iberoamericana 24 (2008), 645-669. [pdf]
[37] P. Hajłasz, P. Koskela, H. Tuominen, Sobolev embeddings, extensions and measure density condition J. Funct. Anal. 254 (2008), 1217--1234. [pdf]
[36] P. Hajłasz, T. Iwaniec, J. Maly, J. Onninen, Weakly differentiable mappings between manifolds. Memoirs Amer. Math. Soc. 899 (2008), 1--72. [pdf]
2007
[35] P. Hajłasz, Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the target. Geom. Funct. Anal. 17 (2007), 435-467. [pdf]
2004
[32] P. Hajłasz, P. Koskela, Formation of cracks under deformations with finite energy. Calc. Var. Partial Differential Equations 19 (2004), 221--227. [pdf]
[31] P. Hajłasz, J. Onninen, On boundedness of maximal functions in Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 29 (2004), no. 1, 167--176.[pdf]
2003
[30] P. Hajłasz, Whitney's example by way of Assouad's embedding. Proc. Amer. Math. Soc. 131 (2003), 3463--3467. [pdf]
[29] P. Hajłasz, A new characterization of the Sobolev space. (Dedicated to Professor Aleksander Pelczynski on the occasion of his 70th birthday.) Studia Math. 159 (2003), 263--275. [pdf]
[28] P. Hajłasz, Sobolev spaces on metric-measure spaces. (Heat kernels and analysis on manifolds, graphs, and metric spaces (Paris, 2002)), 173--218, Contemp. Math. , 338, Amer. Math. Soc., Providence, RI, 2003. [pdf]
2002
[27] P. Hajłasz, J. Maly, Approximation in Sobolev spaces of nonlinear expressions involving the gradient Ark. Mat. 40 (2002), 245--274. [pdf]
[26] B. Bojarski, P. Hajłasz, P. Strzelecki, Improved $C^{k,\lambda}$ approximation of higher order Sobolev functions in norm and capacity. Indiana Univ. Mat. J. 51 (2002), 507--540. [pdf]
2001
[25] P. Hajłasz, Sobolev inequalities, truncation method, and John domains. (Papers on Analysis: A volume dedicated to Olli Martio on the occasion of his 60th birthday.) Report. Univ. Jyvaskyla 83 (2001), 109--126. [pdf]
2000
[24] P. Hajłasz, P. Koskela, Sobolev met Poincare, Memoirs Amer. Math. Soc. 688 (2000), 1--101. [pdf]
[23] B. Franchi, P. Hajłasz, How to get rid of one of the weights in a two weight Poincare inequality?, Ann. Polon. Math 74 (2000), 97--103. [pdf]
[22] P. Hajłasz, Sobolev mappings, co-area fromula and related topics. In: Proceedings on Analysis and Geometry. Novosibirsk: Sobolev Instinute Press, 2000, pp. 227--254. [pdf]
1998
[19] P. Hajłasz, P. Strzelecki, Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces, Math. Ann. 312 (1998), 341-362. [pdf]
[18] P. Hajłasz, P. Koskela, Isoperimetric inequalities and imbedding theorems in irregular domains, J. London Math. Soc. 58 (1998), 425-450. [pdf]
[17] P. Hajłasz, J. Kinnunen, Holder quasicontinuity of Sobolev functions on metric spaces Rev. Mat. Iberoamericana, 14 (1998), 601-622. [pdf]
1997
[16] P.Hajłasz, O. Martio, Traces of Sobolev functions on fractal type sets and characterization of extension domains J. Funct. Anal., 143(1997), 221--246. [pdf]
1996
[15] P. Hajłasz, Sobolev spaces on an arbitrary metric space, Potential Analysis , 5 (1996), 403--415. [pdf]
[14] P. Hajłasz, A counterexample to the $L^p$--Hodge decomposition, Banach Center Publications 33 (1996), 79--83. [pdf]
[13] P. Hajłasz, On approximate differentiability of functions with bounded deformation Manuscripta Math. 91 (1996), 61--72. [pdf]
1995
[12] P. Hajłasz, P. Koskela, Sobolev meets Poincare, C. R. Acad Sci. Paris 320 (1995), 1211--1215. [pdf]
[11] P. Hajłasz, Boundary behaviour of Sobolev mappings, Proc. Amer. Math. Soc. , 123 (1995), 1145-1148. [pdf]
[10] P. Hajłasz, A note on weak approximation of minors, Ann. I. H. P. Analyse non lineaire, 12 (1995), 415-424. [pdf]
[9] P. Hajłasz, Geometric approach to Sobolev spaces and badly degenerate elliptic equations, GAKUTO International Series; Mathematical Sciences and Applications, vol. 7, (1995) pp. 141--168. Nonlinear Analysis and Applications (The Proceedings of Banach Center Minisemester, November-Decembed, 1994) N.Kenmochi, M. Niezgodka, P. Strzelecki eds. [pdf]
[8] P. Hajłasz, A. Kałamajska, Polynomial asymptotics and approximation of Sobolev functions, Studia Math. 113(1995), 55-64. [pdf]
1994
[7] P. Hajłasz, Equivalent statement of the Poincare conjecture, Annali. Mat. Pura Appl. 167 (1994), 25--31. [pdf]
[6] P. Hajłasz, Approximation of Sobolev mappings, Nonlinear Analysis 22 (1994), 1579-1591. [pdf]
[5] P. Hajłasz, A Sard type theorem for Borel mappings, Colloq. Math. 67 (1994), 217--221. [pdf]
1993
[4] B. Bojarski, P. Hajłasz, Pointwise inequalities for Sobolev functions and some applications. Studia Math. 106 (1993), 77-92. [pdf]
[3] P. Hajłasz, Change of variables formula under minimal assumptions. Colloq. Math. 64 (1993), 93-101. [pdf]
[2] P. Hajłasz, Note on Meyers--Serrin's Theorem. Expositiones Math. 11 (1993), 377-379. [pdf]
[1] P. Hajłasz, P. Strzelecki, On the differentiability of solutions of quasilinear elliptic equations, Colloq. Math. 64 (1993), 287-291. [pdf]
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