# Recent preprints and work in progress

### Jean-Pierre Demailly

(last update: June 27, 2018)

[87] * Lars Hörmander and the theory of L² estimates for the d-bar operator*, manuscript Institut Fourier, December 2013,
[hormander_l2_estimates.pdf]

[88] *On the cohomology of pseudoeffective line bundles*, written
exposition of a talk given at the Abel Symposium, Trondheim, July 2013;
manuscript Institut Fourier, January 9, 2014
[psef_cohom_plain_v2.pdf]

[89] *Structure theorems for compact Kähler manifolds with nef
anticanonical bundles*, written exposition of a talk given at the
KSCV10 conference, Gyeong-Ju, Korea, manuscript Institut Fourier,
November 24, 2014, [kscv10.pdf]

[90] *Towards the Green-Griffiths-Lang conjecture*,
manuscript Institut Fourier, December 2, 2014,
[hal-01092537]
[towards_ggl.pdf]

[91] (in collaboration with Hervé Gaussier)
*Algebraic embeddings of smooth almost complex structures*,
manuscript Institut Fourier, December 9, 2014,
[hal-01092620]
[alg_embedding.pdf]

The above manuscript refers to an unpublished work of F.Bogomolov
"Complex manifolds and algebraic foliations" originally published in the
preprint series of RIMS, Kyoto. It seems very hard to find; here is a copy:
[bogomolov_RIMS1084.pdf]

[92] * Yet incomplete attempt of what could be a proof of an optimal version
of the Kobayashi conjecture on the hyperbolicity of very general
hypersurfaces*, manuscript Institut Fourier, February 13, 2015,
[hal-01109166]
[arXiv:1501.07625v3]
[kobayashi_conj.pdf]
(Lemma 5.1.18 is wrong - maybe a suitable weaker result could still
be used instead...)

[93] * Extension of holomorphic functions defined on non reduced analytic
subvarieties*, manuscript Institut Fourier, October 18, 2015,
arXiv : 1510.05230 and
[hal-01216962]
[holom_extension.pdf]

[94] * Variational approach for complex Monge-Ampère equations and
geometric applications (after Berman, Berndtsson, Boucksom, Eyssidieux,
Guedj, Jonsson, Zeriahi, ...)*, Séminaire Bourbaki, March 19, 2016,
exposé no. 1112,
[bourbaki_1112.pdf]

[95] * Precise error estimate of the Brent-McMillan algorithm for the
computation of Euler's constant*, [hal-01377144v2]
[gamma_brent_mcmillan.pdf]

[96] (in collaboration with Junyan Cao and Shin-ichi Matsumura)
* A general extension theorem for cohomology classes on non reduced analytic spaces*, [hal-01480220]
[cohom_class_extension.pdf]

[97] *Fano manifolds with nef tangent bundles are weakly almost
Kähler-Einstein*,
[hal-01660131]
[special_issue_mok.pdf]

[98] *Recent results on the Kobayashi and Green-Griffiths-Lang
conjectures*, expanded version of talks given at the 16th Takagi
Lectures in Tokyo, November 29, 2015,
[hal-01683413]
[takagi16_jpd.pdf]

[99] *A simple proof of the Kobayashi conjecture on the
hyperbolicity of general algebraic hypersurfaces*, chapter of a
forthcoming book by S. Diverio et al on hyperbolicity,
[hypbook_jpd.pdf]

[100] (in collaboration with Mohammad Reza Rahmati) *Morse
cohomology estimates for jet differential operators*
[jets_asympt.pdf]

Research papers (already published)

Books, textbooks & other documents