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Estimates for solutions of Monge-Ampere type equations in the geometriccontext

2021/41/B/ST1/01632

Keywords:

Monge-Ampere equations Complex hessian equations

Descriptors:

  • ST1_011:
  • ST1_004:

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: 3

Call: OPUS 21 - announced on 2021-03-15

Amount awarded: 480 600 PLN

Project start date (Y-m-d): 2022-01-18

Project end date (Y-m-d): 2027-01-17

Project duration:: 60 months (the same as in the proposal)

Project status: Pending project

Project description

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Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Information in the final report

  • Publication in academic press/journals (8)
  • Book publications / chapters in book publications (1)
  1. A remark on Oka's lemma and a geometric property of pseudoconvex domains
    Authors:
    Sławomir Dinew, Żywomir Dinew
    Academic press:
    The Journal of Geometric Analysis (rok: 2024, tom: 34, strony: 23 pp), Wydawca: Springer Nature
    Status:
    Published
    DOI:
    10.1007/s12220-023-01472-x - link to the publication
  2. Weak Solutions to Monge–Ampère Type Equations on Compact Hermitian Manifold with Boundary
    Authors:
    Sławomir Kołodziej, Ngoc Cuong Nguyen
    Academic press:
    The Journal of Geometric Analysis (rok: 2023, tom: 33, strony: 15p), Wydawca: Springer Nature
    Status:
    Published
    DOI:
    10.1007/s12220-022-01054-3 - link to the publication
  3. A variational approach to SKT and balanced metrics
    Authors:
    Sławomir Dinew, Dan Popovici
    Academic press:
    Journal de Mathématiques Pures et Appliquées (rok: 2023, tom: 175, strony: 237–268), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.matpur.2023.05.008 - link to the publication
  4. A SPECIAL CONCAVITY PROPERTY FOR POSITIVE HESSIAN QUOTIENT OPERATORS
    Authors:
    Pengfei Guan, Marcin Sroka
    Academic press:
    Discrete and Continuous Dynamical Systems (rok: 2025, tom: early access, strony: 46033), Wydawca: AIMS
    Status:
    Published
    DOI:
    10.3934/dcds.2025181 - link to the publication
  5. COMPLEX HESSIAN MEASURES WITH RESPECT TO A BACKGROUND HERMITIAN FORM
    Authors:
    Sławomir Kołodziej, Ngoc Cuong Nguyen
    Academic press:
    Analysis & PDE (rok: 2026, tom: 19, strony: 107-166), Wydawca: MSP
    Status:
    Published
    DOI:
    10.2140/apde.2026.19.107 - link to the publication
  6. A remark on the Hölder regularity of solutions to the complex Hessian equation
    Authors:
    Sławomir Kołodziej, Ngoc Cuong Nguyen
    Academic press:
    Journal of Functional Analysis (rok: 2025, tom: 289, strony: Article 111005), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2025.111005 - link to the publication
  7. Remarks on Hessian quotient equations on Riemannian manifolds
    Authors:
    Marci Sroka
    Academic press:
    Journal of Functional Analysis (rok: 2025, tom: 289, strony: article 111123), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2025.111123 - link to the publication
  8. The Dirichlet problem for the Monge–Ampère equation on Hermitian manifolds with boundary
    Authors:
    Sławomir Kołodziej, Cuong Ngoc Nguyen
    Academic press:
    Calculus of Variations and Partial Differential Equations (rok: 2023, tom: 2,58402777777778, strony: 14246), Wydawca: Springer Nature
    Status:
    Published
    DOI:
    10.1007/s00526-022-02336-y - link to the publication
  1. Weak Convergence of Monge-Ampère Measures on Compact Hermitian Manifolds
    Authors:
    Sławomir Kołodziej, Ngoc Cuong Nguyen
    Book:
    Springer Proceedings in Mathematics & Statistics, Complex Geometric Analysis (rok: 2025, tom: 481, strony: 113-124), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/978-981-96-0447-0 - link to the publication

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