Hoang-Chinh Lu

Maître de Conférences

Laboratoire de Mathématiques d'Orsay
Bât. 307 (IMO)
Université Paris-Saclay
91405 Orsay Cedex
France


Courrier électronique :
Bureau : 2A12
Téléphone : (+33) 1 69 15 57 37
Photo

Conferences/Events

Analysis of Monge-Ampère, a tribute to Ahmed Zeriahi May 31- June 04, 2021 Toulouse.




Textes

Habilitation à diriger des recherches

Curriculum Vitae




Projets

Projet ANR JCJC 2021-2024: Paraplui

PEPS CNRS 2019



Enseignement et Encadrement depuis 2016

  1. Co-directeur de thèse pour Quang-Tuan Dang en codirection avec Vincent Guedj.
  2. M2 AAG: TD Géométrie analytique complexe
  3. Encadrement M2, TER M1, Projet L3
  4. TD L3MFA: Fonctions holomorphes (Math 308), Algèbre (Math 303)
  5. Modèles dynamiques en biologie (Math 391)
  6. TD L2 Math: Fonctions de plusieurs variables (Math 205), Analyse (Math 201)
  7. TD L1 Math: Analyse (Math 104)




Preprints et Publications

  1. Geodesic distance and Monge-Ampère measures on contact sets, with E. Di Nezza, arXiv:2112.09627.

  2. Quasi-plurisubharmonic envelopes 3: Solving Monge-Ampère equations on hermitian manifolds, with V. Guedj, preprint arXiv:2107.01938.

  3. Quasi-plurisubharmonic envelopes 2: Bounds on Monge-Ampère volumes, with V. Guedj, preprint arXiv:2106.04272, to appear in Algebraic Geometry.

  4. Quasi-plurisubharmonic envelopes 1: Uniform estimates on Kähler manifolds, with V. Guedj, preprint arXiv:2106.04273.

  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, Final version .

  6. Comparison of Monge-Ampère capacities, Ann. Polon. Math. 126 (2021), no. 1, 31--53, arXiv:2005.04264, Final version .
  7. Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds, with T.T. Phung and T.D. Tô, preprint, to appear in Annales de l'Institut Fourier, 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, preprint, to appear in Annali della Scuola Normale Superiore di Pisa, arXiv:1909.02469,Final version .

  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, to appear in Ann. Sci. l'École Norm. Sup. 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.




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Département de Mathématiques
, Université Paris-Saclay, Bât. 307, F-91405 Orsay Cedex ,France
Last updated on 03 March 2022.