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Publications

  1. Convexity of the Mabuchi functional in big cohomology classes, with S. Trapani, A. Trusiani, (2024) arXiv:2410.08984

  2. Weighted cscK metrics (I): a priori estimates, with S. Jubert, A. Lahdili, (2024) arxiv:2407.09929

  3. Entropy in the relative setting, with S. Trapani, A. Trusiani, SIGMA 20 (2024), 039, 19 pages, arXiv:2310.10152

  4. Relative pluripotential theory on compact Kähler manifolds, with T. Darvas, C. H. Lu, (2023). To appear in Pure and Applied Mathematics Quarterly. (here)

  5. The regularity of envelopes, with Stefano Trapani, Annales scientifiques de l’ENS, volume 57, issue 5 (2024). arXiv:2110.14314

  6. Geodesic distance and Monge-Ampère measures on contact sets, with Chinh Lu, Analysis Math. 48 (2022), no. 2, 451–488. arXiv:2112.09627

  7. Uniform estimates for cscK metrics, with Alix Deruelle, Annales de la Faculté des Sciences de Toulouse, (6) 31 (2022), no. 3, 975–993. (here).

  8. Finite entropy vs finite energy, with V. Guedj, C. Lu, Commentari Mathematici Helvetici, 96 (2021), no. 2, 389–419. arXiv:2006.07061.

  9. Special Metric in Kähler geometry (survey), Bollettino dell’Unione Matematica Italiana (2021), no. 1, 43–49.

  10. Families of singular Kähler-Einstein metrics, with H. Guenancia, V. Guedj, J. Eur. Math. Soc. 25 (2023), no. 7, 2697–2762. arXiv:2003.08178

  11. Monge-Ampére measures on contact sets, with S. Trapani, Math. Research Letters, Vol. 28, No. 5 (2021), pp. 1337-1352. arXiv:1912.12720

  12. The metric geometry of singularity types, with T. Darvas, C. H. Lu, Journal für die reine und angewandte Mathematik, 771 (2021), 137–170. arXiv:1909.00839

  13. L^p metric geometry of big and nef cohomology classes, with C. H. Lu, Acta Mathematica Vietnamica 45 (2020), no. 1, 53–69. arXiv:1808.06308

  14. Log-concavity of volume and complex Monge-Ampère equations with prescribed singularities, with T. Darvas, C. H. Lu, Mathematische Annalen, 1-38, (2021). arXiv:1807.00276

  15. L^1 metric geometry of big cohomology classes, with T. Darvas, C. H. Lu, Ann. Inst. Fourier, 68 (2018), no. 7, 3053–3086. arXiv:1802.00087

  16. Regularity od push-forward of Monge-Ampère measures, with C. Favre, Ann. Inst. Fourier, 68 (2018), no. 7, 2965–2979. arXiv:1712.09884

  17. Monotonicity of non-pluripolar products and complex Monge-Ampère equations with prescribed singularities, with T. Darvas, C. H. Lu, Analysis & PDE,(2018), 2049-2087. arXiv:1705.05796

  18. Geometry and topology of the space of Kähler metrics on singular varieties, with V. Guedj, Compositio Mathematica, 154 (2018), no. 8, 1593–1632. arXiv:1606.07706

  19. The Monge-Ampère class E, contribution in the book ``Complex and Symplectic Geometry”, Springer INDAM Series 21, Springer, 2017, 51-59.

  20. On the singularity type of full mass currents in big cohomogy classes, with T. Darvas, C. Lu, in Compositio Mathematica, Vol. 154 (2018), 380-409. arXiv:1606.01527

  21. Divisorial Zariski Decomposition and some properties of full mass currents, with E. Floris, S. Trapani, Ann. Scuola Normale Superiore, (2017). arXiv:1505.07638

  22. Uniqueness and short time regularity of the weak Kähler-Ricci flow, with C. H. Lu, Advances in Mathematics, Vol. 305C (2016), 953-993. arXiv:1411.7958

  23. Finite Pluricomplex energy measures, Potential Analysis, Vol. 44 (2015), no. 1, 155-167. arXiv:1501.03747

  24. Generalized Monge-Ampère capacities, with C. H. Lu, IMRN, (2015), no. 16, 7287–7322. arXiv:1402.2497

  25. Complex Monge-Ampère equations on quasi-projective varieties, with C. H. Lu, Journal für die reine und angewandte Mathematik, 727 (2017), 145–167. arXiv:1401.6398

  26. Stability of Monge-Ampère energy classes, J. Geom. Anal., Vol. 25 (2015), no. 4, 2565-2589. arXiv:1311.7301

  27. Hitchhiker’s guide to fractional Sobolev spaces, with G. Palatucci, E. Valdinoci, Bulletin des Sciences Mathématique, Vol. 136 (2012) no.5. arXiv:1104.4345