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    Preprints


  1. Kiselman Minimum Principle and Rooftop Envelopes in Complex Hessian Equations, with Per Åhag, Rafał Czyż and Alexander Rashkovskii, arXiv:2405.04948.

  2. Geodesic connectivity and rooftop envelopes in the Cegrell classes, with Per Åhag, Rafał Czyż and Alexander Rashkovskii, arXiv:2405.04384.

  3. Relative pluripotential theory on compact Kähler manifolds, with T. Darvas and E. Di Nezza, arXiv:2303.11584. To appear in Pure and Applied Mathematics Quarterly. Special issue in honor of J.-P. Demailly.

  4. Degenerate complex Hessian equations on compact Hermitian manifolds, with V. Guedj, arXiv:2302.03354. To appear in Pure and Applied Mathematics Quarterly. Special issue in honor of J.-P. Demailly.

  5. Quasi-plurisubharmonic envelopes 1: Uniform estimates on Kähler manifolds, with V. Guedj, arXiv:2106.04273. To appear in J. Eur. Math. Soc.


    Articles


  1. Quasi-plurisubharmonic envelopes 3: Solving Monge-Ampère equations on hermitian manifolds, with V. Guedj, J. Reine Angew. Math. 800 (2023), 259--298. arXiv:2107.01938.

  2. Plurisigned hermitian metrics, with D. Angella and V. Guedj, Trans. Amer. Math. Soc. 376 (2023), 4631--4659. arXiv:2207.04705.

  3. Quasi-plurisubharmonic envelopes 2: Bounds on Monge-Ampère volumes, with V. Guedj, Algebr. Geom. 9, No. 6, 688--713 (2022). arXiv:2106.04272.

  4. Geodesic distance and Monge-Ampère measures on contact sets, with E. Di Nezza, Anal. Math. 48 (2022), no. 2, 451--488. arXiv:2112.09627.

  5. Finite entropy vs finite energy, with E. Di Nezza and V. Guedj, Comment. Math. Helv. 96 (2021), no. 2, 389--419. arXiv:2006.07061 .

  6. Comparison of Monge-Ampère capacities, Ann. Polon. Math. 126 (2021), no. 1, 31--53. arXiv:2005.04264.

  7. Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds, with T.T. Phung and T.D. Tô, Ann. Inst. Fourier (Grenoble) 71 (2021), no. 5, 2019--2045. arXiv:2003.08417.

  8. Pluripotential solutions versus viscosity solutions to complex Monge-Ampère flows, with V. Guedj and A. Zeriahi, Pure and Applied Mathematics Quarterly 17-3 (2021), 971--990. arXiv:1909.07069.

  9. Complex Hessian equations with prescribed singularity on compact Kähler manifolds, with V.D. Nguyen, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 23 (2022), no. 1, 425--462. arXiv:1909.02469.

  10. The metric geometry of singularity types, with T. Darvas and E. Di Nezza, J. Reine Angew. Math. 771 (2021), 137--170. arXiv:1909.00839.

  11. Geodesic stability, the space of rays, and uniform convexity in Mabuchi geometry, with T. Darvas, Geom. Topol. 24, No. 4, 1907--1967 (2020). arXiv:1810.04661.

  12. Pluripotential Kähler-Ricci flows, with V. Guedj and A. Zeriahi, Geom. Topol. 24 (2020), no. 3, 1225--1296. arXiv:1810.02121.

  13. The pluripotential Cauchy-Dirichlet problem for complex Monge-Ampère flows, with V. Guedj and A. Zeriahi, Ann. Sci. l'École Norm. Sup. (4) 54 (2021), no. 4, 889--944. arXiv:1810.02122.

  14. Stability of solutions to complex Monge-Ampère flows , with V. Guedj and A. Zeriahi, Annales de l'Institut Fourier, Tome 68 (2018) no. 7, pp. 2819--2836. arXiv:1810.02123.

  15. Lp metric geometry of big and nef cohomology classes, with E. Di Nezza, Acta Math Vietnam 45, 53--69 (2020). arXiv:1808.06308.

  16. Pluripotential Theory and Convex Bodies: Large Deviation Principle, with T. Bayraktar, T. Bloom and N. Levenberg, Ark. Mat. Volume 57, Number 2 (2019), 247--283. arXiv:1807.11369.

  17. Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity, with T. Darvas and E. Di Nezza, Math. Ann. 379, No. 1-2, 95-132 (2021). arXiv:1807.00276.

  18. Quantization in geometric pluripotential theory, with T. Darvas and Y. Rubinstein, Commun. Pure Appl. Math. 73, No. 5, 1100--1138 (2020). arXiv:1806.03800.

  19. L1 metric geometry of big cohomology classes , with T. Darvas and E. Di Nezza, Annales de l'Institut Fourier, Tome 68, no 7 (2018), p. 3053--3086. arXiv:1802.00087.

  20. Monotonicity of non-pluripolar products and complex Monge-Ampère equations with prescribed singularity, with T. Darvas and E. Di Nezza, Analysis & PDE 11 (2018) 2049--2087. arXiv:1705.05796.

  21. Weak subsolutions to complex Monge-Ampère equation, with V. Guedj and A. Zeriahi, J. Math. Soc. Japan, Volume 71, Number 3 (2019), 727--738. arXiv:1703.06728.

  22. Plurisubharmonic envelopes and supersolutions, with V. Guedj and A. Zeriahi, J. Differential Geom. Volume 113, Number 2 (2019), 273--313. arXiv:1703.05254.

  23. On the singularity type of full mass currents in big cohomology classes , with T. Darvas and E. Di Nezza, Compositio Mathematica, 154 (2), 380--409. arXiv:1606.01527.

  24. From the Kähler-Ricci flow to moving free boundaries and shocks, with R. Berman, Journal de l'École polytechnique--Mathématiques, Tome 5 (2018), pp. 519--563. arXiv:1604.03259.

  25. Regularity of weak minimizers of the K-energy and applications to properness and K-stability, with R. Berman and T. Darvas, Ann. Sci. l'École Norm. Sup. 53, 2020, 267--289. arXiv:1602.03114.

  26. Convexity of the extended K-energy and the large time behavior of the weak Calabi flow, with R. Berman and T. Darvas, Geom. Topol. Volume 21, Number 5 (2017), 2945--2988. arXiv:1510.01260.

  27. Uniqueness and short time regularity of the weak Kähler-Ricci flow, with E. Di Nezza, Adv. Math. 305 (2017), 953--993. arXiv:1411.7958.

  28. Mixed Hessian inequalities and uniqueness in the class $\mathcal{E}(X,\omega,m)$, with S. Dinew, Math. Z. 279 (2015), no. 3-4, 753--766. arXiv:1404.6202.

  29. Degenerate complex Hessian equations on compact Kähler manifolds, with V.D. Nguyen, Indiana Univ. Math. J. 64 (2015), no. 6, 1721--1745. arXiv:1402.5147.

  30. Generalized Monge-Ampère capacities, with E. Di Nezza, Int. Math. Res. Not. IMRN 2015, no. 16, 7287--7322. arXiv:1402.2497.

  31. Complex Monge-Ampère equations on quasi-projective varieties, with E. Di Nezza, J. Reine Angew. Math. 727 (2017), 145--167. arXiv:1401.6398.

  32. A variational approach to complex Hessian equations in $\mathbb{C}^n$, J. Math. Anal. Appl. 431 (2015), no. 1, 228--259. arXiv:1301.6502.

  33. Viscosity solutions to complex Hessian equations, J. Funct. Anal. 264 (2013), no. 6, 1355--1379. arXiv:1209.5343.

  34. Solutions to degenerate complex Hessian equations, J. Math. Pures Appl. (9) 100 (2013), no. 6, 785--805. arXiv:1202.2436.