Tomasz Adamowicz's Page

Associate Professor in the Department of Differential Equations

dr hab., prof. IMPAN

Institute of Mathematics Polish Academy of Sciences in Warsaw (IM PAN)

Phone: 22 522 81 80, 510

Email: T(dot)Adamowicz(at)impan(dot)pl

Research Interests

 

Seminar in Geometric Function and Mapping Theory at IM PAN

Archival seminars in Geometric Function and Mapping Theory at IM PAN (2013-2016)

 

Geometry and analysis on metric surfaces

 

Simons Semester in Geometry and analysis in function and mapping theory on Euclidean and metric measure spaces at IM PAN,
September-November 2019

Geometric analysis and related topics /in honour of Tadeusz Iwaniec's 70th birthday

Geometric Function Theory meets Geometric Group Theory in Warsaw, Banach Center, IM PAN, 14-17 Oct 2015

Research meeting in Variable exponent theory and applications, Banach Center, IM PAN, 26-29 Oct 2014

Banach Center Publications, Volume 101: Calculus of Variations and PDEs

Grants:

Grant Sonata 5 by NCN (Narodowe Centrum Nauki/National Science Center), 2014-2017, UMO 2013/09/D/ST1/03681

Grant Iuventus Plus by Ministry of Science and Higher Education, 2015-2017, Nr 0009/IP3/2015/73

Grant OPUS 13 by NCN (Narodowe Centrum Nauki/National Science Center), 2018-2021, UMO-2017/25/B/ST1/01955

Grant PRELUDIUM BIS 2 by NCN (Narodowe Centrum Nauki/National Science Center), 2021-2025,

PhD Students:

Editorial service:

Analysis and Mathematical Physics

Publications and submitted manuscripts:

  1. Hardy spaces and quasiregular mappings (with M.J. Gonzalez)

    submitted

  2. Isoperimetric inequalities and regularity of A-harmonic functions on surfaces (with G. Veronelli)

    Calc. Var. PDEs, 63, article no. 48, 2024, doi.org/10.1007/s00526-023-02651-y

  3. Strong Liouville theorems for discrete averaging operators (with José G. Llorente)

    submitted

  4. Hardy spaces and quasiconformal maps in the Heisenberg group (with K. Faessler)

    J. Functional Analysis, 284(6) 2023, Paper No. 109832, 68pg.

  5. Schwarzians on the Heisenberg group (with B. Warhurst)

    submitted

    6. Asymptotically mean value harmonic functions in doubling metric measure spaces (with A. Kijowski and E. Soultanis)

    The manuscript is split into two parts:

  6. Asymptotically mean value harmonic functions in doubling metric measure spaces

    Analysis and Geometry in Metric Spaces, 10(1) (2022), 344–372. doi.org/10.1515/agms-2022-0143

  7. Asymptotically mean value harmonic functions in subriemannian and RCD settings

    The Journal of Geometric Analysis, 33(3) (2023), Paper No. 80. doi.org/10.1007/s12220-022-01132-6

  8. Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces (with G. Veronelli)

    Calc. Var. PDEs, 61(1) 2022, Paper No. 2, doi.org/10.1007/s00526-021-02109-z

  9. Hardy spaces for quasiregular mappings and composition operators (with M.J. Gonzalez)

    The Journal of Geometric Analysis, 31(11) 2021, 11417-11427, doi.org/10.1007/s12220-021-00687-0

  10. Variational approach to the asymptotic mean-value property for the p-Laplacian on Carnot groups (with A. Kijowski, A. Pinamonti and B. Warhurst)

    Nonlinear Analysis, Vol. 198 September 2020, doi.org/10.1016/j.na.2020.111893

  11. The Rado-Kneser-Choquet theorem for p-harmonic mappings between Riemannian surfaces (with J. Jääskeläinen, A. Koski)

    Rev. Math. Iberoam., 36(6) 2020 doi.org/10.4171/rmi/1183

  12. A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group (with K. Faessler and B. Warhurst)

    Ann. Mat. Pura Appl., 199 2020, 147-186, doi.org/10.1007/s10231-019-00871-8

  13. Mean value property and harmonicity on Carnot-Caratheodory groups (with B. Warhurst)

    Potential Anal., 52 2020, 497-525, doi.org/10.1007/s11118-018-9740-4

  14. Harmonic functions on metric measure spaces (with M. Gaczkowski and P. Górka)

    Rev. Math. Complut., 32(1) 2019, 141-186, doi.org/10.1007/s13163-018-0272-7

  15. The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg property (with N. Shanmugalingam)

    Math. Zeit., Vol. 293, Issue 3-4 2019, 1633-1656 doi.org/10.1007/s00209-019-02268-y

  16. Prime ends in metric spaces and boundary extensions of mappings

    Anal. Math. Phys., 9 2019, 1941-1975, doi.org/10.1007/s13324-019-00292-z

  17. Prime ends in the Heisenberg group H1 and the boundary behavior of quasiconformal mappings (with B. Warhurst)

    Ann. Acad. Sci. Fenn. Math., 43(2) 2018, 1-38

  18. Three-spheres theorems for subelliptic quasilinear equations in Carnot groups of Heisenberg-type (with B. Warhurst)

    Proceedings of AMS 144(10) 2016, 4291-4302.

  19. The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(.)-harmonic measures (with N. Lundström)

    Ann. Mat. Pura Appl. , 195(2) 2016, 623-658 doi: 10.1007/s10231-015-0481-3

  20. Hölder continuity of quasiminimizers with nonstandard growth (with O. Toivanen)

    Nonlinear Anal. Vol. 125, September 2015, 433-456

  21. The Liouville theorems for elliptic equations with nonstandard growth (with P. Górka)

    Commun. Pure Appl. Anal. 14(6) 2015, 2377-2392.

  22. Three-spheres theorem for p-harmonic mappings

    Calc. Var. PDEs, 53(3) 2015, 1015-1032, doi: 10.1007/s00526-014-0775-0

  23. Maximal operator in variable exponent Lebesgue spaces on unbounded quasimetric measure spaces (with P. Harjulehto and P. Hästö)

    Math. Scand. 116 (1), 2015, 5-22

  24. The geometry of planar p-harmonic mappings: convexity, level curves and the isoperimetric inequality

    Ann. Sc. Norm. Super. Pisa. Volume XIV(1), 2015, 263-292, doi: 10.2422/2036-2145.201201_010

  25. Phragmen-Lindelöf theorems for equations with nonstandard growth

    Nonlinear Anal. Vol. 97, March 2014, 169-184

  26. Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points (with A. Björn, J. Björn)

    Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (6), 2014, 1131-1153, doi: 10.1016/j.anihpc.2013.07.012

  27. Prime ends for domains in metric spaces (with A. Björn, J. Björn, N. Shanmugalingam)

    Adv. Math. 238 (2013) , 459-505

  28. Remarks on time map for quasilinear equations (with P. Korman)

    J. Math. Anal. Appl. Volume 376, Issue 2, 15 April 2011, 686-695

  29. Harnack's Inequality and The Strong p(x)-Laplacian (with P. Hästö)

    J. Differential Equations, Volume 250, Issue 3, 1 February 2011, 1631-1649

  30. Non-conformal Loewner type estimates for modulus of curve families (with N. Shanmugalingam)

    Ann. Acad. Sci. Fenn. Math., (35), (2010), 609-626

  31. Maximum principles and nonexistence results for radial solutions to equations involving p-Laplacian (with A. Kałamajska)

    Math. Methods Appl. Sci., Volume 33, Issue 13, (2010), 1618-1627

  32. Mappings of finite distortion and PDE with nonstandard growth (with P. Hästö)

    Int. Math. Res. Not. IMRN, (2010), 1940-1965,doi:10.1093/imrn/rnp192

  33. On p-harmonic mappings in the plane

    Nonlinear Anal., Volume 71, Issues 1-2, 1 July 2009-15 July 2009, 502-511

  34. On a variant of the maximum principle involving radial p-Laplacian with applications to nonlinear eigenvalue problems and nonexistence results (with A. Kałamajska)

    Topol. Methods Nonlinear Anal., Volume 34, no. 1, (2009), 1-20

  35. The Grötzsch problem in higher dimensions

    Rend. Lincei Mat. Appl. (18) (2007), 163-177

Teaching

Some of my teaching evaluations are available here (1 - min, 5 - max):

Spring 2003, Fall 2003: Linear Algebra with Geometry. (Recitations)

Fall 2005, Fall 2006: Calculus 1. (Recitations)

Spring 2007, Fall 2007, Spring 2008: Calculus 3.

Fall 2008: Calculus 2.

Winter 2009: Calculus 3.

Spring 2009: Calculus 4

(Section 1), Calculus 4 (Section 2).

Fall 2009: Differential Equations (Section 1), Differential Equations (Section 2).

Winter 2010: Calculus 1.

Spring 2010: Calculus 2.

Fall(1st half) 2011, 2012: Flervariabelanalys (Calculus 3-4)

Fall(2nd half) 2010, 2011: Envariabelanalys 1 (Calculus 1)

Fall 2011, 2012: Linear Algebra

Winter 2011, 2012, 2013: Envariabelanalys 2 (Calculus 2-3)

Spring 2011, 2012, 2013: Flervariabelanalys (Calculus 3-4)

Some links

Institute of Mathematics Polish Academy of Sciences in Warsaw

Department of Mathematics, Linköping University

Graduate Student Seminar at University of Cincinnati

Department of Mathematical Sciences, University of Cincinnati

Mathematics Graduate Organization (MGO) at Syracuse University

Department of Mathematics, Syracuse University

Faculty of Mathematics, Informatics and Mechanics, University of Warsaw

Banach Center, Poland