Research

arXiv ORCID
I am interested in differential and complex geometry.
Some specific topics are: Complex Monge-Ampère Equations, Kaehler-Einstein metrics, Kaehler-Ricci Flow, Chern-Ricci Flow, Pluripotential Theory.

Preprints and publications

  1. Regularity of solutions to Monge--Ampère equations on compact Hermitian manifolds
    [arXiv]
  2. Modulus of continuity of Monge--Ampère potentials in big cohomology classes (w. Hoang-Son Do, Hoang Hiep Pham)
    [arXiv] to appear in Indiana Univ. Math. J.
  3. Singularities vs non-pluripolar Monge--Ampère masses (w. Hoang-Son Do, Hoang Hiep Pham)
    [arXiv] [DOI] Math. Z. 311, 47 (2025).
  4. An iterative construction of complete Kaehler--Einstein metrics (w. Tat Dat Tô)
    [arXiv] to appear in Publ. RIMS Kyoto Univ.
  5. Hermitian null loci
    [arXiv] to appear in Trans. Amer. Math. Soc.
  6. Kaehler-Einstein metrics on quasi-projective manifolds (w. Duc-Viet Vu)
    [arXiv] [DOI] Math. Ann. 392, 4071–4103 (2025)
  7. Singularities of the Chern-Ricci flow
    [arXiv] [DOI] Anal. PDE 19-3 (2026), 449--483.
  8. Continuity of Monge-Ampère potentials with prescribed singularities
    [arXiv] [DOI] J. Geom. Anal. 33, 318 (2023).
  9. Pluripotential Chern-Ricci Flows
    [arXiv] [DOI] Indiana Univ. Math. J. 73 No. 4 (2024), 1401–1441.
  10. Continuity of Monge-Ampere Potentials in Big Cohomology Classes
    [arXiv] [DOI] Int. Math. Res. Not. 14, 11180–11201 (2022).
  11. Pluripotential Monge-Ampere Flows in big cohomology classes
    [arXiv] [DOI] J. Funct. Anal. 282(6), 65 (2022).

Talks

Miscellaneous