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Hessian type equation in complex geometry

2013/08/A/ST1/00312

Keywords

Descriptors

  • ST1_8: Analiza
  • ST1_4: Geometria algebraiczna i zespolona

Panel

ST1 – Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution

Uniwersytet Jagielloński, Wydział Matematyki i Informatyki

Voivodeship: małopolskie

Other projects carried out by the institution »

Principal investigator (from the host institution)

prof. Sławomir Kołodziej

Number of co-investigators in the project: 9

Call

MAESTRO 4 – announced on 2012-12-15

Amount awarded
2 043 900 PLN
Project start date
2013-09-17
Project end date
2019-09-16
Project duration
72 months (the same as in the proposal)
Project status
Project settled

Equipment purchased [PL]

  1. Laptop. Cost: 25 000 PLN

Information in the final report

Publication in academic press/journals (36)

  1. The Richberg Technique for Subsolutions

    Authors:
    F. R. Harvey, H. B. Lawson Jr. S. Pliś
    Academic press:
    Communications in Analysis and Geometry (year: 2020, volume: 28, pages: 1787-1806), Publisher: International Press of Boston
    Status:
    Published

  2. Weak solutions of complex Hessian equations on compact Hermitian manifolds

    Authors:
    Sławomir Kołodziej, Ngoc Cuong Nguyen
    Academic press:
    Compositio Mathematica (year: 2016, volume: 152, pages: 2221-2248), Publisher: London Math Soc
    Status:
    Published
    DOI:
    10.1112/S0010437X16007417 – link to the publication

  3. On the Błocki–Zwonek conjectures

    Authors:
    Per Ahag i Rafał Czyż
    Academic press:
    Complex Variables and Elliptic Equations (year: 2015, volume: 60, pages: 1270-1276), Publisher: Taylor & Francis Group
    Status:
    Published
    DOI:
    10.1080/17476933.2015.1004541 – link to the publication

  4. A very special EPW sextic and two IHS fourfolds

    Authors:
    Maria Donten-Bury, Bert van Geemen, Grzegorz Kapustka, Michał Kapustka, Jarosław A. Wiśniewski
    Academic press:
    Geom. Topol. (year: 2017, volume: 21, pages: 1179-1230), Publisher: Mathematical Sciences Publishers
    Status:
    Published

  5. The geometry of C^2 equipped with Warren's metric

    Authors:
    Szymon Myga
    Academic press:
    Annales Polonici Mathematici (year: 2018, volume: 121, pages: 243-249), Publisher: Polish Acad Sciences Inst. Mathematics
    Status:
    Published
    DOI:
    10.4064/ap180618-28-8 – link to the publication

  6. Extension and approximation of msubharmonic functions

    Authors:
    Per Ahag, Rafał Czyż, Lisa Hed
    Academic press:
    Complex Var. Elliptic Equ. (year: 2018, volume: 63, pages: 783-801), Publisher: Taylor & Francis Group
    Status:
    Published
    DOI:
    10.1080/17476933.2017.1345888 – link to the publication

  7. A characterization of Cegrell's classes and generalized m-capacities

    Authors:
    Van Thien Nguyen
    Academic press:
    Annales Polonici Mathematici (year: 2018, volume: 121, pages: 33-43), Publisher: Polish Acad Sciences Inst. Mathematics
    Status:
    Published
    DOI:
    10.4064/ap170728-26-1 – link to the publication

  8. Smooth approximation of plurisubharmonic functions on almost complex manifolds

    Authors:
    F. Reese Harvey, H. Blaine Lawson Jr. i Szymon Pliś
    Academic press:
    Mathematische Annalen (year: 2016, volume: 366, pages: 929-940), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00208-015-1348-z – link to the publication

  9. A viscosity approach to the Dirichlet problem for degenerate complex Hessian type equations

    Authors:
    Sławomir Dinew, Hoang-Son Do, Tat Dat To
    Academic press:
    Anal. PDE (year: 2019, volume: 12, pages: 505-535), Publisher: MSP
    Status:
    Published
    DOI:
    10.2140/apde.2019.12.505 – link to the publication

  10. Hölder continuous solutions of the Monge-Ampere equation on compact Hermitian manifolds

    Authors:
    Sławomir Kołodziej, Ngoc Cuong Nguyen
    Academic press:
    Ann. Inst. Fourier (year: 2018, volume: 68, pages: 2951-2964), Publisher: -
    Status:
    Published
    DOI:
    10.5802/aif.3232 – link to the publication

  11. The geometry of m-hyperconvex domains

    Authors:
    Per Ahag, Rafał Czyż, Lisa Hed
    Academic press:
    J. Geom. Anal. (year: 2018, volume: 28, pages: 3196-3222), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s12220-017-9957-2 – link to the publication

  12. Mixed Hessian inequalityies and uniqueness in $mathcal E (X,omega,m)$

    Authors:
    S. Dinew, H. Ch. Lu
    Academic press:
    Mathematische Zeitschrift (year: 2015, volume: 279, pages: 753-766), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00209-006-0067-2 – link to the publication

  13. Regularity of degenerate Hessian Equations

    Authors:
    S. Dinew, Sz. Pliś, X. Wang
    Academic press:
    Calc Var. PDE (year: 2019, volume: 58:138, pages: 46043), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00526-019-1574.4 – link to the publication

  14. Hessian boundary measures

    Authors:
    Van Thien Nguyen
    Academic press:
    International Journal of Mathematics (year: 2019, volume: online, pages: 46039), Publisher: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0129167X19500162 – link to the publication

  15. Alexandrov-Bakelman-Pucci type estimate for plurisubharmonic functions

    Authors:
    Sławomir Dinew i Żywomir Dinew
    Academic press:
    International Mathematics Research Notices (year: 2020, volume: -, pages: 46033), Publisher: Oxford Academic
    Status:
    Published
    DOI:
    10.1093/imrn/rnaa151 – link to the publication

  16. Pluripotential theory on compact Hermitian manifolds

    Authors:
    Sławomir Dinew
    Academic press:
    Annales de la Faculté des Sciences de Toulouse (year: 2016, volume: 25, pages: 91-139), Publisher: Universite Paul Sabatier
    Status:
    Published
    DOI:
    10.5802/afst.1488 – link to the publication

  17. The complex Monge-Ampere type equation on compact Hermitian manifolds and Applications

    Authors:
    Ngoc Cuong Nguyen
    Academic press:
    Advances in Mathematics (year: 2016, volume: 286, pages: 240-285), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2015.09.009 – link to the publication

  18. Vector spaces of delta-plurisubharmonic functions and extensions of the complex Monge–Ampère operator

    Authors:
    Per Ahag, Urban Cegrell, Rafał Czyż
    Academic press:
    Journal of Mathematical Analysis and Applications (year: 2015, volume: 422, pages: 960–980), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2009.07.013 – link to the publication

  19. Stability and regularity of solutions of the Monge-Ampère equation on Hermitian manifolds

    Authors:
    Sławomir Kołodziej, Ngoc Cuong Nguyen
    Academic press:
    Advances in Mathematics (year: 2019, volume: 346, pages: 264-304), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2019.02.004 – link to the publication

  20. Verra Four-Folds, Twisted Sheaves, and the Last Involution

    Authors:
    Chiara Camere, Grzegorz Kapustka, Michał Kapustka and Giovanni Mongardi
    Academic press:
    Int. Math. Res. Notices (year: 2018, volume: -, pages: 18264), Publisher: Oxford academic
    Status:
    Published
    DOI:
    10.1093/imrn/rnx327 – link to the publication

  21. Equivalence of K3 surfaces from Verra threefolds

    Authors:
    Grzegorz Kapustka, Michał Kapustka, Riccardo Moschetti
    Academic press:
    Kyoto journal of mathematics (year: 2020, volume: 60 (4), pages: 1209-1226), Publisher: DUKE UNIV PRESS
    Status:
    Published
    DOI:
    10.1215/21562261-2019-0059 – link to the publication

  22. Non standard properties of m-subharmonic functions

    Authors:
    Sławomir Dinew i Sławomir Kołodziej
    Academic press:
    Dolomites Research Notes on Approximation (year: 2018, volume: 11, pages: 35-50), Publisher: Padova University Pres
    Status:
    Published
    DOI:
    10.14658/pupj-drna-2018-4-4 – link to the publication

  23. The classification of holomorphic (m, n)-subharmonic morphisms

    Authors:
    Per Ahag, Rafał Czyż and Lisa Hed
    Academic press:
    Complex Variables and Elliptic Equations (year: 2019, volume: online, pages: 46045), Publisher: Taylor & Francis Group
    Status:
    Published
    DOI:
    10.1080/17476933.2019.1574773 – link to the publication

  24. On a characterization of m-subharmonic functions with weak singularities

    Authors:
    Per Ahag and Rafał Czyż
    Academic press:
    Annales Polonici Mathematici (year: 2018, volume: online, pages: 46031), Publisher: Polish Acad Sciences Inst. Mathematics
    Status:
    Published
    DOI:
    10.4064/ap180628-10-9 – link to the publication

  25. Weak solutions of the Monge-Ampere equation on compact Hermitian manifolds

    Authors:
    Sławomir Kołodziej
    Academic press:
    International Journal of Mathematics (year: 2017, volume: 28, no. 9, pages: 46045), Publisher: World Scientific Publishing Company
    Status:
    Published
    DOI:
    10.1142/S0129167X1740002X – link to the publication

  26. On the Błocki–Zwonek conjectures and beyond

    Authors:
    Per Ahag i Rafał Czyż
    Academic press:
    Archiv der Mathematik (year: 2015, volume: 105, pages: 371-380), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00013-015-0810-1 – link to the publication

  27. On delta m-subharmonic functions

    Authors:
    Van Thien Nguyen
    Academic press:
    Annales Polonici Mathematici (year: 2016, volume: 118, pages: 25-49), Publisher: Polish Acad Sciences Inst. Mathematics
    Status:
    Published
    DOI:
    10.4064/ap3959-9-2916 – link to the publication

  28. EPW cubes

    Authors:
    A.Iliev, G.Kapustka, M.Kapustka, K.Ranestad
    Academic press:
    Journal fur die reine und angewandte Mathematik (year: 2018, volume: -, pages: 46047), Publisher: Walter de Gruyter & CO
    Status:
    Published
    DOI:
    10.1515/crelle-2016-0044 – link to the publication

  29. A Counterexample to a Conjecture by Błocki–Zwonek

    Authors:
    P. Ahag , R. Czyż, and P. H. Lundow
    Academic press:
    Experimental Mathematics (year: 2018, volume: 27, pages: 119-124), Publisher: A K Peters LTD
    Status:
    Published
    DOI:
    10.1080/10586458.2016.1230913 – link to the publication

  30. On the complex Monge-Ampere operator in unbounded domains

    Authors:
    P. Ahag and R. Czyż
    Academic press:
    Universitatis Jagiellonicae Acta Mathematica (year: 2017, volume: 54, pages: 46216), Publisher: Wydawnictwo Uniwersytetu Jagiellońskiego
    Status:
    Published
    DOI:
    10.4467/20843828AM.17.001.7077 – link to the publication

  31. Remarks on Mukai threefolds admitting $C^{*}$ action

    Authors:
    Sławomir Dinew, Grzegorz Kapustka, Michał Kapustka
    Academic press:
    Moscow Mathematical Journal (year: 2017, volume: 17, pages: 15-33), Publisher: Independent Univ Moscow
    Status:
    Published

  32. The convexity of radially symmetric $m$-subharmonic functions

    Authors:
    Van Thien Nguyen
    Academic press:
    Complex. Var. Elliptic. Equ. (year: 2018, volume: 63, pages: 1396-1407), Publisher: Taylor & Francis Group
    Status:
    Published
    DOI:
    10.1080/17476933.2017.1373347 – link to the publication

  33. On $m$-subharmonic ordering of measures

    Authors:
    Van Thien Nguyen
    Academic press:
    Results in Mathematics (year: 2018, volume: 73, pages: 46040), Publisher: Birkhauser Verlag AG
    Status:
    Published
    DOI:
    10.1007/s00025-018-0765-1 – link to the publication

  34. On a constant in the energy estimate

    Authors:
    Rafał Czyż, Van Thien Nguyen
    Academic press:
    Comptes Rendus Math. (year: 2017, volume: 355, pages: 1050-1054), Publisher: Elsevier France-Editions Scientifiques Medicales Elsevier
    Status:
    Published
    DOI:
    10.1016/j.crma.2017.09.019 – link to the publication

  35. The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary

    Authors:
    Dongwei Gu, Ngoc Cuong Nguyen
    Academic press:
    Annali della Scuola Normale Superiore di Pisa (year: 2018, volume: 18, pages: 1189-1248), Publisher: Scuola Normale Superiore
    Status:
    Published
    DOI:
    10.2422/2036-2145.201606_013 – link to the publication

  36. The minimum sets and free boundaries of strictly plurisubharmonic functions

    Authors:
    Sławomir Dinew, Żywomir Dinew
    Academic press:
    Calculus of Variations and Partial Differential Equations (year: 2016, volume: 55, pages: 46039), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00526-016-1069-5 – link to the publication

Book publications / chapters in book publications (1)

  1. AN INEQUALITY BETWEEN COMPLEX HESSIAN MEASURES OF HOLDER CONTINUOUS m-SUBHARMONIC FUNCTIONS AND CAPACITY

    Authors:
    Sławomir Kołodziej, Ngoc Cuong Nguyen
    Book:
    Geometric Analysis In Honor of Gang Tian's 60th Birthday (year: 2019, volume: 333, pages: 157-166), Publisher: Birkhauser
    Status:
    Published

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