Comptes Rendus
no. 4
Complex analysis/Analytic geometry
A new proof of Kiselman's minimum principle for plurisubharmonic functions
[Une nouvelle démonstration du principe du minimum de Kiselman pour les fonctions pluri-sous-harmoniques]

Présenté par : Jean-Pierre Demailly

Fusheng Deng1 ; Zhiwei Wang2 ; Liyou Zhang3 ; Xiangyu Zhou1, 4
1 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
2 School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, PR China
3 School of Mathematical Sciences, Capital Normal University, Beijing, 100048, PR China
4 Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, PR China
Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 345-348.

Nous donnons une nouvelle démonstration du principe du minimum de Kiselman pour les fonctions pluri-sous-harmoniques. Elle s'inspire de la régularisation des fonctions pluri-sous-harmoniques de Demailly, en utilisant le théorème d'extension d'Ohsawa–Takegoshi.

We give a new proof of Kiselman's minimum principle for plurisubharmonic functions, inspired by Demailly's regularization of plurisubharmonic functions by using Ohsawa–Takegoshi's extension theorem.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.04.006
Fusheng Deng 1 ; Zhiwei Wang 2 ; Liyou Zhang 3 ; Xiangyu Zhou 1, 4

1 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
2 School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, PR China
3 School of Mathematical Sciences, Capital Normal University, Beijing, 100048, PR China
4 Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, PR China 
@article{CRMATH_2019__357_4_345_0,
     author = {Fusheng Deng and Zhiwei Wang and Liyou Zhang and Xiangyu Zhou},
     title = {A new proof of {Kiselman's} minimum principle for plurisubharmonic functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {345--348},
     publisher = {Elsevier},
     volume = {357},
     number = {4},
     year = {2019},
     doi = {10.1016/j.crma.2019.04.006},
     language = {en},
}
TY  - JOUR
AU  - Fusheng Deng
AU  - Zhiwei Wang
AU  - Liyou Zhang
AU  - Xiangyu Zhou
TI  - A new proof of Kiselman's minimum principle for plurisubharmonic functions
JO  - Comptes Rendus. Mathématique
PY  - 2019
SP  - 345
EP  - 348
VL  - 357
IS  - 4
PB  - Elsevier
DO  - 10.1016/j.crma.2019.04.006
LA  - en
ID  - CRMATH_2019__357_4_345_0
ER  - 
%0 Journal Article
%A Fusheng Deng
%A Zhiwei Wang
%A Liyou Zhang
%A Xiangyu Zhou
%T A new proof of Kiselman's minimum principle for plurisubharmonic functions
%J Comptes Rendus. Mathématique
%D 2019
%P 345-348
%V 357
%N 4
%I Elsevier
%R 10.1016/j.crma.2019.04.006
%G en
%F CRMATH_2019__357_4_345_0
Fusheng Deng; Zhiwei Wang; Liyou Zhang; Xiangyu Zhou. A new proof of Kiselman's minimum principle for plurisubharmonic functions. Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 345-348. doi : 10.1016/j.crma.2019.04.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.04.006/

[1] B. Berndtsson Prekopa's theorem and Kiselman's minimum principle for plurisubharmonic functions, Math. Ann., Volume 312 (1998), pp. 785-792

[2] J.-P. Demailly Regularization of closed positive currents and intersection theory, J. Algebraic Geom., Volume 1 (1992) no. 3, pp. 361-409

[3] F. Deng; Z. Wang; L. Zhang; X. Zhou New characterization of plurisubharmonic functions and positivity of direct image sheaves | arXiv

[4] F. Deng; H. Zhang; X. Zhou Positivity of direct images of positively curved volume forms, Math. Z., Volume 278 (2014), pp. 347-362

[5] F. Deng; H. Zhang; X. Zhou Positivity of character subbundles and minimumprinciple for noncompact group actions, Math. Z., Volume 286 (2017), pp. 431-442

[6] C. Kiselman The partial Legendre transformation for plurisubharmonic functions, Invent. Math., Volume 49 (1978) no. 2, pp. 137-148

[7] T. Ohsawa; K. Takegoshi On the extension of L2 holomorphic functions, Math. Z., Volume 195 (1987) no. 2, pp. 197-204

Cité par Sources :

☆ The authors are partially supported respectively by NSFC grants [NSFC-11871451], [NSFC-11701031], [NSFC-11671270], [NSFC-11688101]. The second author was partially supported by the Fundamental Research Funds for the Central Universities.

Commentaires - Politique

Ces articles pourraient vous intéresser

Lelong numbers, complex singularity exponents, and Siu's semicontinuity theorem

Qi'an Guan; Xiangyu Zhou

C. R. Math (2017)

On the Ohsawa–Takegoshi L2 extension theorem and the twisted Bochner–Kodaira identity

Qiʼan Guan; Xiangyu Zhou; Langfeng Zhu

C. R. Math (2011)

Optimal constant problem in the L2 extension theorem

Qiʼan Guan; Xiangyu Zhou

C. R. Math (2012)