A new proof of Kiselman's minimum principle for plurisubharmonic functions

Fusheng Deng; Zhiwei Wang; Liyou Zhang; Xiangyu Zhou

doi:10.1016/j.crma.2019.04.006

Complex analysis/Analytic geometry

A new proof of Kiselman's minimum principle for plurisubharmonic functions

Presented by: Jean-Pierre Demailly

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

Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 345-348.

Abstract
Résumé

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.

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.

Received: 2019-01-02
Accepted: 2019-04-12
Published online: 2019-04-01

DOI: 10.1016/j.crma.2019.04.006

Author's affiliations:

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/

References
Cited by

[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 $L^{2}$ holomorphic functions, Math. Z., Volume 195 (1987) no. 2, pp. 197-204

Cited by 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.

Comments - Policy