Simons Semester in Geometric Analysis

at IMPAN

• Jun-Jul 2026

University of Warsaw’s Excellence Initiative - Research University (IDUB)

Thematic Research Program Geometric Analysis: Methods and Applications GAMA25

• Feb-Dec 2025

University of Warsaw’s Excellence Initiative - Research University (IDUB)

Thematic Research Program Geometric Analysis and PDEs

• Feb-Dec 2024

NCN Grant Opus no. 2019/35/B/ST1/02030

Metody topologiczne analizy geometrycznej (Topological methods in geometric analysis)

• 2020-25
• Popularno-naukowe streszczenie projektu (in Polish)
• Description of the project for the general public

Team members: P.G., Dr. Zofia Grochulska, Dr. Michał Miśkiewicz.

research project Mobility Plus no 603/MOB/2011/0
of Polish Ministry of Science and Higher Education

Nieliniowe zagadnienia eliptyczne i subeliptyczne z krytyczną nieliniowością: konstrukcje funkcji próbnych i problem słabej domkniętości przestrzeni słabych rozwiązań, ((Nonlinear elliptic and subelliptic problems with critical nonlinearity: constructions of test functions and weak compactness of solutions))

• 2011-12

(updated October 2025)

1. Behnam Esmayli; Paweł Goldstein; Piotr Hajłasz Differentiability of Lipschitz mappings into metric spaces: area and co-area formulas, submitted.
2. Paweł Goldstein; Piotr Hajłasz C²-Lusin approximation of convex functions: one variable case, J. Math. Anal. Appl., Volume 557, Issue 2, 15 May 2026, 130333, doi.
3. Paweł Goldstein; Zofia Grochulska; Piotr Hajłasz Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms, Expositiones Math. 43(4), July 2025, 125681, doi.
4. Paweł Goldstein; Zofia Grochulska; Piotr Hajłasz Constructing diffeomorphisms and homeomorphisms with prescribed derivative, Adv. Math. 460 (2025), 110020, doi.
5. Paweł Goldstein; Piotr Hajłasz Smooth approximation of mappings with rank of the derivative at most 1, Calc. Var. Partial Differential Equations 62 (2023), no. 3, Art. 88, 22 pp., doi.
6. Paweł Goldstein; Piotr Hajłasz Jacobians of W^1,p homeomorphisms, case p=[n/2], Calc. Var. Partial Differential Equations 58 (2019), no. 4, Art. 122, 28 pp., doi.
7. Paweł Goldstein; Piotr Hajłasz C¹ mappings in R⁵ with rank Df ≤ 3 cannot be uniformly approximated by C² mappings with rank Df ≤ 3, J. Math. Anal. Appl. 468(2), 15 December 2018, 1108–1114, doi.
8. Paweł Goldstein; Piotr Hajłasz; Pekka Pankka Topologically nontrivial counterexamples to the Sard theorem, International Mathematics Research Notices (2018), rny179, doi.
9. Paweł Goldstein; Piotr Hajłasz Topological obstructions to continuity of Orlicz-Sobolev mappings of finite distortion, Ann. Mat. Pura Appl. (2018), doi.
10. Paweł Goldstein; Zofia Grochulska; Chang-Yu Guo; Pekka Koskela; Debandjan Nandi Characterizations of generalized John domains in Rⁿ via metric duality, Colloquium Mathematicum 176 (2024), 87–105.
11. Paweł Goldstein; Anna Zatorska-Goldstein Uhlenbeck's decomposition in Sobolev and Morrey-Sobolev spaces, Results Math. (2018) 73:71.
12. Paweł Goldstein; Piotr Hajłasz Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian, Ann. Acad. Sci. Fenn. Math. 43 (2018), 147–170.
13. Paweł Goldstein; Piotr Hajłasz; Mohammad Reza Pakzad Finite Distortion Sobolev Mappings between Manifolds are Continuous, Int. Math. Res. Not. IMRN 2019, no. 14, 4370–4391.
14. Paweł Goldstein; Piotr Hajłasz A measure and orientation preserving homeomorphism of a cube with Jacobian equal -1 almost everywhere, Arch. Ration. Mech. Anal. 225 (2017), no. 1, 65–88.
15. Paweł Goldstein; Paweł Strzelecki; Anna Zatorska-Goldstein Weak compactness of solutions for fourth order elliptic systems with critical growth, Studia Math. 214 (2013), no. 2, 137–156.
16. Paweł Goldstein; Piotr Hajłasz Sobolev mappings, degree, homotopy classes and rational homology spheres, J. Geom. Anal. 22 (2012), no. 2, 320–338.
17. Paweł Goldstein Gradient flow of a harmonic function in R3, J. Differential Equations 247 (2009), no. 9, 2517–2557.
18. Paweł Goldstein; Paweł Strzelecki; Anna Zatorska-Goldstein On polyharmonic maps into spheres in the critical dimension, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 4, 1387–1405.
19. Paweł Goldstein On the long-time behaviour of solutions of the p-Laplacian parabolic system, Colloq. Math. 113 (2008), no. 2, 267–278.
20. Paweł Goldstein; Anna Zatorska-Goldstein Calderon-Zygmund type estimates for nonlinear systems with quadratic growth on the Heisenberg group, Forum Math. 20 (2008), no. 4, 679–710.
21. Paweł Goldstein Kovalevska vs. Kovacic—two different notions of integrability and their connections, Differential Galois theory (Będlewo, 2001), 63–73, Banach Center Publ., 58, Polish Acad. Sci., Warsaw, 2002.