Paweł Goldstein


Research grant

NCN Grant Opus nr 2019/35/B/ST1/02030
Metody topologiczne analizy geometrycznej (Topological methods in geometric analysis).

Popularno-naukowe streszczenie projektu.
Description of the project for the general public.

Two master scholarships (10 months, 1000 PLN/month) are planned within the project. The call for applications will be announced in May 2022.


  1. Paweł Goldstein; Piotr Hajłasz Jacobians of W1,p homeomorphisms, case p=[n/2], Calc. Var. Partial Differential Equations 58 (2019), no. 4, Art. 122, 28 pp.
  2. 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. Volume 468, Issue 2, 15 December 2018, Pages 1108-1114,
  3. Paweł Goldstein; Piotr Hajłasz; Pekka Pankka Topologically nontrivial counterexamples to the Sard theorem, International Mathematics Research Notices (2018), rny179,
  4. Paweł Goldstein; Piotr Hajłasz Topological obstructions to continuity of Orlicz-Sobolev mappings of finite distortion Ann. Mat. Pura Appl. (2018).
  5. Paweł Goldstein; Chang-Yu Guo; Pekka Koskela; Debandjan Nandi Characterizations of generalized John domains in Rn via metric duality preprint, submitted
  6. Paweł Goldstein; Anna Zatorska-Goldstein Uhlenbeck's decomposition in Sobolev and Morrey-Sobolev spaces Results Math (2018) 73:71
  7. Paweł Goldstein; Piotr Hajłasz Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian. Ann. Acad. Sci. Fenn. Math., Vol 43 (2018), pp. 147-170.
  8. 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.
  9. 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.
  10. 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
  11. Paweł Goldstein; Piotr Hajłasz Sobolev mappings, degree, homotopy classes and rational homology spheres. J. Geom. Anal. 22 (2012), no. 2, 320–338.
  12. Paweł Goldstein Gradient flow of a harmonic function in R3. J. Differential Equations 247 (2009), no. 9, 2517–2557.
  13. 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.
  14. Paweł Goldstein On the long-time behaviour of solutions of the p-Laplacian parabolic system. Colloq. Math. 113 (2008), no. 2, 267–278.
  15. 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.
  16. 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.