Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Hessian type equation in complex geometry

2013/08/A/ST1/00312

Keywords:

m-subharmonic functions complex Hessian equations complex singularity exponents Hemitian Kähler and Kähler-Einstein manifolds Kähler-Ricci flow cone metrics

Descriptors:

  • ST1_8: Analysis
  • ST1_4: Algebraic and complex geometry

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

woj. 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 (Y-m-d): 2013-09-17

Project end date (Y-m-d): 2019-09-16

Project duration:: 72 months (the same as in the proposal)

Project status: Project completed

Equipment purchased [PL]

  1. Laptop (25 000 PLN)

Information in the final report

  • Publication in academic press/journals (39)
  • Book publications / chapters in book publications (1)
  1. 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 (rok: 2015, tom: 422, strony: 960–980), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2009.07.013 - link to the publication
  2. Pluripotential theory on compact Hermitian manifolds
    Authors:
    Sławomir Dinew
    Academic press:
    Annales de la Faculté des Sciences de Toulouse (rok: 2016, tom: 25, strony: 91-139), Wydawca: Universite Paul Sabatier
    Status:
    Published
    DOI:
    10.5802/afst.1488 - link to the publication
  3. On a characterization of m-subharmonic functions with weak singularities
    Authors:
    Per Ahag and Rafał Czyż
    Academic press:
    Annales Polonici Mathematici (rok: 2018, tom: online, strony: 45666), Wydawca: Polish Acad Sciences Inst. Mathematics
    Status:
    Published
    DOI:
    10.4064/ap180628-10-9 - link to the publication
  4. A Counterexample to a Conjecture by Błocki–Zwonek
    Authors:
    P. Ahag , R. Czyż, and P. H. Lundow
    Academic press:
    Experimental Mathematics (rok: 2018, tom: 27, strony: 119-124), Wydawca: A K Peters LTD
    Status:
    Published
    DOI:
    10.1080/10586458.2016.1230913 - link to the publication
  5. The convexity of radially symmetric $m$-subharmonic functions
    Authors:
    Van Thien Nguyen
    Academic press:
    Complex. Var. Elliptic. Equ. (rok: 2018, tom: 63, strony: 1396-1407), Wydawca: Taylor & Francis Group
    Status:
    Published
    DOI:
    10.1080/17476933.2017.1373347 - link to the publication
  6. Non standard properties of m-subharmonic functions
    Authors:
    Sławomir Dinew i Sławomir Kołodziej
    Academic press:
    Dolomites Research Notes on Approximation (rok: 2018, tom: 11, strony: 35-50), Wydawca: Padova University Pres
    Status:
    Published
    DOI:
    10.14658/pupj-drna-2018-4-4 - link to the publication
  7. The complex Monge-Ampere type equation on compact Hermitian manifolds and Applications
    Authors:
    Ngoc Cuong Nguyen
    Academic press:
    Advances in Mathematics (rok: 2016, tom: 286, strony: 240-285), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2015.09.009 - link to the publication
  8. On the complex Monge-Ampere operator in unbounded domains
    Authors:
    P. Ahag and R. Czyż
    Academic press:
    Universitatis Jagiellonicae Acta Mathematica (rok: 2017, tom: 54, strony: 45851), Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
    Status:
    Published
    DOI:
    10.4467/20843828AM.17.001.7077 - link to the publication
  9. The classification of holomorphic (m, n)-subharmonic morphisms
    Authors:
    Per Ahag, Rafał Czyż and Lisa Hed
    Academic press:
    Complex Variables and Elliptic Equations (rok: 2019, tom: online, strony: 45680), Wydawca: Taylor & Francis Group
    Status:
    Published
    DOI:
    10.1080/17476933.2019.1574773 - link to the publication
  10. Equivalence of K3 surfaces from Verra threefolds
    Authors:
    Grzegorz Kapustka, Michał Kapustka, Riccardo Moschetti
    Academic press:
    Kyoto journal of mathematics (rok: 2020, tom: 60 (4), strony: 1209-1226), Wydawca: DUKE UNIV PRESS
    Status:
    Published
    DOI:
    10.1215/21562261-2019-0059 - link to the publication
  11. Hessian boundary measures
    Authors:
    Van Thien Nguyen
    Academic press:
    International Journal of Mathematics (rok: 2019, tom: online, strony: 45674), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0129167X19500162 - link to the publication
  12. Hölder continuous solutions of the Monge-Ampere equation on compact Hermitian manifolds
    Authors:
    Sławomir Kołodziej, Ngoc Cuong Nguyen
    Academic press:
    Ann. Inst. Fourier (rok: 2018, tom: 68, strony: 2951-2964), Wydawca: -
    Status:
    Published
    DOI:
    10.5802/aif.3232 - link to the publication
  13. On a constant in the energy estimate
    Authors:
    Rafał Czyż, Van Thien Nguyen
    Academic press:
    Comptes Rendus Math. (rok: 2017, tom: 355, strony: 1050-1054), Wydawca: Elsevier France-Editions Scientifiques Medicales Elsevier
    Status:
    Published
    DOI:
    10.1016/j.crma.2017.09.019 - link to the publication
  14. A characterization of Cegrell's classes and generalized m-capacities
    Authors:
    Van Thien Nguyen
    Academic press:
    Annales Polonici Mathematici (rok: 2018, tom: 121, strony: 33-43), Wydawca: Polish Acad Sciences Inst. Mathematics
    Status:
    Published
    DOI:
    10.4064/ap170728-26-1 - link to the publication
  15. On $m$-subharmonic ordering of measures
    Authors:
    Van Thien Nguyen
    Academic press:
    Results in Mathematics (rok: 2018, tom: 73, strony: 45675), Wydawca: Birkhauser Verlag AG
    Status:
    Published
    DOI:
    10.1007/s00025-018-0765-1 - link to the publication
  16. Remarks on Mukai threefolds admitting $C^{*}$ action
    Authors:
    Sławomir Dinew, Grzegorz Kapustka, Michał Kapustka
    Academic press:
    Moscow Mathematical Journal (rok: 2017, tom: 17, strony: 15-33), Wydawca: Independent Univ Moscow
    Status:
    Published
    DOI:
    brak - link to the publication
  17. Weak solutions of the Monge-Ampere equation on compact Hermitian manifolds
    Authors:
    Sławomir Kołodziej
    Academic press:
    International Journal of Mathematics (rok: 2017, tom: 28, no. 9, strony: 45680), Wydawca: World Scientific Publishing Company
    Status:
    Published
    DOI:
    10.1142/S0129167X1740002X - link to the publication
  18. Regularity of degenerate Hessian Equations
    Authors:
    S. Dinew, Sz. Pliś, X. Wang
    Academic press:
    Calc Var. PDE (rok: 2019, tom: 58:138, strony: 45678), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00526-019-1574.4 - link to the publication
  19. The Richberg Technique for Subsolutions
    Authors:
    F. R. Harvey, H. B. Lawson Jr. S. Pliś
    Academic press:
    Communications in Analysis and Geometry (rok: 2020, tom: 28, strony: 1787-1806), Wydawca: International Press of Boston
    Status:
    Published
    DOI:
    brak - link to the publication
  20. The geometry of m-hyperconvex domains
    Authors:
    Per Ahag, Rafał Czyż, Lisa Hed
    Academic press:
    J. Geom. Anal. (rok: 2018, tom: 28, strony: 3196-3222), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s12220-017-9957-2 - link to the publication
  21. The minimum sets and free boundaries of strictly plurisubharmonic functions
    Authors:
    Sławomir Dinew, Żywomir Dinew
    Academic press:
    Calculus of Variations and Partial Differential Equations (rok: 2016, tom: 55, strony: 45674), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00526-016-1069-5 - link to the publication
  22. The smoothing of m-subharmonic functions
    Authors:
    Szymon Pliś
    Academic press:
    - (rok: 2016, tom: -, strony: -), Wydawca: -
    Status:
    Submitted
    DOI:
    - - link to the publication
  23. 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 (rok: 2018, tom: 18, strony: 1189-1248), Wydawca: Scuola Normale Superiore
    Status:
    Published
    DOI:
    10.2422/2036-2145.201606_013 - link to the publication
  24. Alexandrov-Bakelman-Pucci type estimate for plurisubharmonic functions
    Authors:
    Sławomir Dinew i Żywomir Dinew
    Academic press:
    International Mathematics Research Notices (rok: 2020, tom: -, strony: 45668), Wydawca: Oxford Academic
    Status:
    Published
    DOI:
    10.1093/imrn/rnaa151 - link to the publication
  25. Weak solutions of complex Hessian equations on compact Hermitian manifolds
    Authors:
    Sławomir Kołodziej, Ngoc Cuong Nguyen
    Academic press:
    Compositio Mathematica (rok: 2016, tom: 152, strony: 2221-2248), Wydawca: London Math Soc
    Status:
    Published
    DOI:
    10.1112/S0010437X16007417 - link to the publication
  26. On the Błocki–Zwonek conjectures and beyond
    Authors:
    Per Ahag i Rafał Czyż
    Academic press:
    Archiv der Mathematik (rok: 2015, tom: 105, strony: 371-380), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00013-015-0810-1 - link to the publication
  27. The geometry of C^2 equipped with Warren's metric
    Authors:
    Szymon Myga
    Academic press:
    Annales Polonici Mathematici (rok: 2018, tom: 121, strony: 243-249), Wydawca: Polish Acad Sciences Inst. Mathematics
    Status:
    Published
    DOI:
    10.4064/ap180618-28-8 - link to the publication
  28. Extension and approximation of msubharmonic functions
    Authors:
    Per Ahag, Rafał Czyż, Lisa Hed
    Academic press:
    Complex Var. Elliptic Equ. (rok: 2018, tom: 63, strony: 783-801), Wydawca: Taylor & Francis Group
    Status:
    Published
    DOI:
    10.1080/17476933.2017.1345888 - link to the publication
  29. 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 (rok: 2018, tom: -, strony: 18264), Wydawca: Oxford academic
    Status:
    Published
    DOI:
    10.1093/imrn/rnx327 - link to the publication
  30. A Generalised Volume Invariant for Aeppli Cohomology Classes of Hermitian-Symplectic Metrics
    Authors:
    Sławomir Dinew, Dan Popovici
    Academic press:
    Advances in Mathematics , Wydawca: Elsevier
    Status:
    Submitted
    DOI:
    brak - link to the publication
  31. EPW cubes
    Authors:
    A.Iliev, G.Kapustka, M.Kapustka, K.Ranestad
    Academic press:
    Journal fur die reine und angewandte Mathematik (rok: 2018, tom: -, strony: 45682), Wydawca: Walter de Gruyter & CO
    Status:
    Published
    DOI:
    10.1515/crelle-2016-0044 - link to the publication
  32. On delta m-subharmonic functions
    Authors:
    Van Thien Nguyen
    Academic press:
    Annales Polonici Mathematici (rok: 2016, tom: 118, strony: 25-49), Wydawca: Polish Acad Sciences Inst. Mathematics
    Status:
    Published
    DOI:
    10.4064/ap3959-9-2916 - link to the publication
  33. 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 (rok: 2019, tom: 12, strony: 505-535), Wydawca: MSP
    Status:
    Published
    DOI:
    10.2140/apde.2019.12.505 - link to the publication
  34. On the relative capacity on almost complex surface
    Authors:
    Szymon Pliś
    Academic press:
    - (rok: 2018, tom: -, strony: 45682), Wydawca: -
    Status:
    Submitted
    DOI:
    brak - link to the publication
  35. 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. (rok: 2017, tom: 21, strony: 1179-1230), Wydawca: Mathematical Sciences Publishers
    Status:
    Published
    DOI:
    brak - link to the publication
  36. Smooth approximation of plurisubharmonic functions on almost complex manifolds
    Authors:
    F. Reese Harvey, H. Blaine Lawson Jr. i Szymon Pliś
    Academic press:
    Mathematische Annalen (rok: 2016, tom: 366, strony: 929-940), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00208-015-1348-z - link to the publication
  37. Stability and regularity of solutions of the Monge-Ampère equation on Hermitian manifolds
    Authors:
    Sławomir Kołodziej, Ngoc Cuong Nguyen
    Academic press:
    Advances in Mathematics (rok: 2019, tom: 346, strony: 264-304), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2019.02.004 - link to the publication
  38. On the Błocki–Zwonek conjectures
    Authors:
    Per Ahag i Rafał Czyż
    Academic press:
    Complex Variables and Elliptic Equations (rok: 2015, tom: 60, strony: 1270-1276), Wydawca: Taylor & Francis Group
    Status:
    Published
    DOI:
    10.1080/17476933.2015.1004541 - link to the publication
  39. Mixed Hessian inequalityies and uniqueness in $\mathcal E (X,\omega,m)$
    Authors:
    S. Dinew, H. Ch. Lu
    Academic press:
    Mathematische Zeitschrift (rok: 2015, tom: 279, strony: 753-766), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00209-006-0067-2 - link to the publication
  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 (rok: 2019, tom: 333, strony: 157-166), Wydawca: Birkhauser
    Status:
    Published

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